In mathematics, nouns are called numbers and variables. distance from an object Solution: There are many options, but here are a few to think about. Example: Rewrite P = 2x/ 2xw with alternative multiplication symbols. 9 _ 3^3 3 ~ ~3~ I- c) This is a proper fraction; |2 = §^§|f = - Ordering Rational Numbers To order rational numbers is to arrange them according to a set of directions, such as ascending (lowest to highest) or descending (highest to lowest). A variable is a symbol, usually an English letter, written to replace an unknown or changing quantity. Solution: P = 2x/ 2xw can be written as P = 2 • / 2 • w It can also be written as P = 2/ 2w. Ordering rational numbers is useful when determining which unit cost is the cheapest. Any form of reproduction of this book in any format or medium, in whole or in sections must include the referral attribution link (placed in a visible location) in addition to the following terms. [3((-3) 2 - l) 2 - (-3) 4 12] 5(-3) 3 - 1 The potential error here is that you may forget a sign or a set of parentheses, especially if the expression is long or complicated. Also, making a table and drawing a graph are often used together. Matthew estimates his crew will have the crop harvested in 20 hours. The discussion in this lesson revolves around rational numbers. Except as otherwise noted, all CK-12 Content (including CK-12 Curriculum Material) is made available to Users in accordance with the Creative Commons Attribution/Non-Commercial/Share Alike 3.0 Un- ported (CC-by-NC-SA) License ( generation textbooks Authors Andrew Gloag, Anne Gloag, Melissa Kramer Editor Annamaria Farbizio 1 Expressions, Equations, and Functions 1 1.1 Variable Expressions 1 1.2 Order of Operations 6 1.3 Patterns and Expressions 11 1.4 Equations and Inequalities 14 1.5 Functions as Rules and Tables 19 1.6 Functions as Graphs 25 1.7 A Problem-Solving Plan 36 1.8 Problem-Solving Strategies: Make a Table; Look for a Pattern 40 1.9 Chapter 1 Review 44 1.10 Chapter 1 Test 47 2 Properties of Real Numbers 49 2.1 Integers and Rational Numbers 49 2.2 Addition of Rational Numbers 55 2.3 Subtraction of Rational Numbers 59 2.4 Multiplication of Rational Numbers 62 2.5 The Distributive Property 67 2.6 Division of Rational Numbers 70 2.7 Square Roots and Real Numbers 73 2.8 Problem-Solving Strategies: Guess and Check and Work Backwards 77 2.9 Chapter 2 Review 80 2.10 Chapter 2 Test 83 3 Linear Equations 84 3.1 One-Step Equations 85 3.2 Two-Step Equations 89 3.3 Multi-Step Equations 93 3.4 Equations with Variables on Both Sides 96 3.5 Ratios and Proportions 99 3.6 Scale and Indirect Measurement 103 3.7 Percent Problems 108 3.8 Problem-Solving Strategies: Use a Formula 113 3.9 Chapter 3 Review 115 3.10 Chapter 3 Test 117 4 Graphing Linear Equations and Functions 119 4.1 The Coordinate Plane 119 4.2 Graphs of Linear Equations 125 4.3 Graphs Using Intercepts 131 4.4 Slope and Rate of Change 137 4.5 Graphs Using Slope-Intercept Form 144 4.6 Direct Variation 149 4.7 Linear Function Graphs 154 4.8 Problem-Solving Strategies: Read a Graph; Make a Graph 159 4.9 Chapter 4 Review 163 4.10 Chapter 4 Test 167 5 Writing Linear Equations 169 5.1 Linear Equations in Slope-Intercept Form 169 5.2 Linear Equations in Point-Slope Form 177 5.3 Linear Equations in Standard Form 182 5.4 Equations of Parallel and Perpendicular Lines 186 5.5 Fitting a Line to Data 192 5.6 Predicting with Linear Models 201 5.7 Problem-Solving Strategies: Use a Linear Model 207 5.8 Problem-Solving Strategies: Dimensional Analysis 212 5.9 Chapter 5 Review 215 5.10 Chapter 5 Test 217 6 Linear Inequalities and Absolute Value; An Introduction to Probability 219 6.1 Inequalities Using Addition and Subtraction 219 6.2 Inequalities Using Multiplication and Division 224 6.3 Multi-Step Inequalities 227 111 Compound Inequalities 232 6.5 Absolute Value Equations 238 6.6 Absolute Value Inequalities 243 6.7 Linear Inequalities in Two Variables 245 6.8 Theoretical and Experimental Probability 253 6.9 Chapter 6 Review 258 6.10 Chapter 6 Test 260 7 Systems of Equations and Inequalities; Counting Methods 262 7.1 Linear Systems by Graphing 262 7.2 Solving Systems by Substitution 268 7.3 Solving Linear Systems by Addition or Subtraction 275 7.4 Solving Linear Systems by Multiplication 278 7.5 Special Types of Linear Systems 283 7.6 Systems of Linear Inequalities 289 7.7 Probability and Permutations 297 7.8 Probability and Combinations 300 7.9 Chapter 7 Review 303 7.10 Chapter 7 Test 306 8 Exponents and Exponential Functions 308 8.1 Exponential Properties Involving Products 308 8.2 Exponential Properties Involving Quotients 311 8.3 Zero, Negative, and Fractional Exponents 314 8.4 Scientific Notation 317 8.5 Exponential Growth Functions 321 8.6 Exponential Decay Functions 326 8.7 Geometric Sequences and Exponential Functions 331 8.8 Problem-Solving Strategies 334 8.9 Chapter 8 Review 336 8.10 Chapter 8 Test 338 9 Polynomials and Factoring; More on Probability 339 9.1 Addition and Subtraction of Polynomials 339 9.2 Multiplication of Polynomials 345 9.3 Special Products of Polynomials 350 9.4 Polynomial Equations in Factored Form 353 9.5 Factoring Quadratic Expressions 358 9.6 Factoring Special Products 362 9.7 Factoring Polynomials Completely 365 9.8 Probability of Compound Events 370 9.9 Chapter 9 Review 373 9.10 Chapter 9 Test 375 10 Quadratic Equations and Functions 377 10.1 Graphs of Quadratic Functions 377 10.2 Solving Quadratic Equations by Graphing 385 10.3 Solving Quadratic Equations Using Square Roots 391 10.4 Solving Quadratic Equations by Completing the Square 394 10.5 Solving Quadratic Equations Using the Quadratic Formula 399 10.6 The Discriminant 403 10.7 Linear, Exponential, and Quadratic Models 407 10.8 Problem-Solving Strategies: Choose a Function Model 413 10.9 Chapter 10 Review 417 l O.l OChapter 10 Test 420 11 Radicals and Geometry Connections; Data Analysis 422 11.1 Graphs of Square Root Functions 422 11.2 Radical Expressions 426 11.3 Radical Equations 432 11.4 The Pythagorean Theorem and its Converse 436 11.5 The Distance and Midpoint Formulas 441 11.6 Measures of Central Tendency and Dispersion 447 11.7 Stem- and-Leaf Plots and Histograms 454 11.8 Box-and- Whisker Plots 461 11.9 Chapter 11 Review 467 ll.l OChapter 11 Test 469 12 Rational Equations and Functions; Statistics 471 12.1 Inverse Variation Models 471 12.2 Graphs of Rational Functions 474 12.3 Division of Polynomials 480 V Rational Expressions 483 12.5 Multiplication and Division of Rational Expressions 487 12.6 Addition and Subtraction of Rational Expressions 490 12.7 Solution of Rational Equations 495 12.8 Surveys and Samples 499 12.9 Chapter 12 Review 509 12.10Chapter 12 Test 511 Chapter 1 Expressions, Equations, and Functions The study of expressions, equations, and functions is the basis of mathematics. Make sure you check your input before writing your answer. The "writing an equation" strategy is the one you will work with the most frequently in your study of algebra. This doesn't make sense because Jeff is already 10. How many ears of corn will his crew harvest per hour? Definition: A rational number is a number that can be written in the form |, where a and b are integers 49 b ± 0. If the dimensions of the pasture are 300 feet by 225 feet, how much fencing should the ranch hand purchase to enclose the pasture? Find the unit cost and order the rational numbers in ascending order. 3x9_27 4x7_28 ~" 63 ~ ~~ 7x9 9x7 63 Because 28 f For more information regarding how to order fractions, watch this You Tube video.

What could you use to quickly find out how much money you would earn for different hours of work? For example, sum, addition, more than, and plus all mean to add numbers together. Definition: To evaluate means to follow the verbs in the math sentence. To begin to evaluate a mathematical expression, you must first substitute a number for the variable. Solution: Evaluate means to follow the directions, which is to take 7 times y and subtract 11. When we have canceled all common factors, we have a fraction in its simplest form. Example: What variables would be choices for the following situations? The following is a real-life example that shows the importance of evaluating a mathematical variable. Example 2: Cans of tomato sauce come in three sizes: 8 ounces, 16 ounces, and 32 ounces.

What could you use to quickly find out how much money you would earn for different hours of work? For example, sum, addition, more than, and plus all mean to add numbers together. Definition: To evaluate means to follow the verbs in the math sentence. To begin to evaluate a mathematical expression, you must first substitute a number for the variable. Solution: Evaluate means to follow the directions, which is to take 7 times y and subtract 11. When we have canceled all common factors, we have a fraction in its simplest form.

Example: What variables would be choices for the following situations? The following is a real-life example that shows the importance of evaluating a mathematical variable. Example 2: Cans of tomato sauce come in three sizes: 8 ounces, 16 ounces, and 32 ounces. $1.29 ounce ' 32 Arranging the rational numbers in ascending order: 0.0403125, 0.061875, 0.07375 Example 3: Which is greater | or |?

Example: To prevent major accidents or injuries, these horses must be fenced in a rectangular pasture. The costs for each size are $0.59, $0.99, and $1.29, respectively. Solution: Begin by creating a common denominator for these two fractions. 7 X 9 = 63, therefore the common denominator is 63.

Throughout this chapter, you will learn how to choose the best variables to describe a situation, simplify an expression using the Order of Operations, describe functions in various ways, write equations, and solve problems using a systematic approach. When someone is having trouble with algebra, they may say, "I don't speak math! You can also use a graphing calculator to evaluate expressions with more than one variable. Press [ENTER] to obtain the answer —.88 or _8 9" Practice Set Sample explanations for some of the practice exercises below are available by viewing the following video. When you are familiar with all of the problem-solving strategies, it is up to you to choose the methods that you are most comfortable with and that make sense to you. Set up an equation, draw a diagram, make a chart, or construct a table as a start to begin your problem-solving plan. Step 4: Check and Interpret: Check to see if you have used all your information. Solve Real- World Problems Using a Plan Example 1: Jeff is 10 years old. How old will Jeff be when he is twice as old as Ben? How many ears of corn will his crew harvest per hour? It will take 20 hours to harvest the entire field, so we need to divide 198,000 by 20 to get the number of ears picked per hour. Suppose Matthew's crew takes 36 hours to harvest the field. • Improper fractions are rational numbers where the numerator is greater than the denominator. A frog is sitting perfectly on top of number 7 on a number line. 93 Multi-Step Equations by Combining Like Terms In the last lesson, you learned the definition of like terms and how to combine such terms. This situation has several pieces of information: soda cans, slices of pizza, and party favors. 3p 4p 37 = 79 This equation requires three steps to solve. Use the Addition Property of Equality to get the variable on one side of the equal sign and the numerical values on the other. Apply the Addition Property of Equality: 7p 37 - 37 = 79 - 37. Apply the Multiplication Property of Equality: 7p 4- 7 = 42 -f 7. This lesson will show you how to use the Distributive Property to solve multi-step equations. Solution: Apply the Distributive Property: l Ox 18 = 78. Note that there is not always a match between the number of the practice exercise in the video and the number of the practice exercise listed in the following exercise set.

" While this may seem weird to you, it is a true statement. 3x 2 -4y 2 x 4 Evaluate the expression: — — — ~[ x for x = -2, y 1. Note that there is not always a match between the number of the practice exercise in the video and the number of the practice exercise listed in the following exercise set. (3 7) -=-(7-12) 4 2-(3 (2-l)) (0 ~x 4 ' 4-(6 2) ^ °J 5. In this book, we will often use more than one method to solve a problem. You could draw a picture (it may take a while), write an equation, look for a pattern, or make a table. We need to figure out how many ears of corn are in the field. 198,000 20 9,900 The crew can harvest 9,900 ears per hour. Improper fractions can be rewritten as a mixed number - an integer plus a proper fraction. The frog jumps randomly to the left or right, but always jumps a distance of exactly 2. Evaluate the following expression: |d 7a 2 ; use a = (-1), d = 24. The length of a rectangle is one more inch than its width. We will use the following situation to further demonstrate solving equations involving like terms. You will need to provide 3 cans of soda per person, 4 slices of pizza per person, and 37 party favors. In general, to solve any equation you should follow this procedure. Remove any parentheses by using the Distributive Property or the Multiplication Property of Equality. Simplify each side of the equation by combining like terms. Apply the Addition Property of Equality: 10* 18 - 18 = 78 - 18. Apply the Multiplication Property of Equality: l Ox -f 10 = 60 4- 10. However, the practice exercise is the same in both.

||What could you use to quickly find out how much money you would earn for different hours of work? For example, sum, addition, more than, and plus all mean to add numbers together. Definition: To evaluate means to follow the verbs in the math sentence. To begin to evaluate a mathematical expression, you must first substitute a number for the variable. Solution: Evaluate means to follow the directions, which is to take 7 times y and subtract 11. When we have canceled all common factors, we have a fraction in its simplest form. Example: What variables would be choices for the following situations? The following is a real-life example that shows the importance of evaluating a mathematical variable. Example 2: Cans of tomato sauce come in three sizes: 8 ounces, 16 ounces, and 32 ounces. $1.29 ounce ' 32 Arranging the rational numbers in ascending order: 0.0403125, 0.061875, 0.07375 Example 3: Which is greater | or |? Example: To prevent major accidents or injuries, these horses must be fenced in a rectangular pasture. The costs for each size are $0.59, $0.99, and $1.29, respectively. Solution: Begin by creating a common denominator for these two fractions. 7 X 9 = 63, therefore the common denominator is 63. Throughout this chapter, you will learn how to choose the best variables to describe a situation, simplify an expression using the Order of Operations, describe functions in various ways, write equations, and solve problems using a systematic approach. When someone is having trouble with algebra, they may say, "I don't speak math! You can also use a graphing calculator to evaluate expressions with more than one variable. Press [ENTER] to obtain the answer —.88 or _8 9" Practice Set Sample explanations for some of the practice exercises below are available by viewing the following video. When you are familiar with all of the problem-solving strategies, it is up to you to choose the methods that you are most comfortable with and that make sense to you. Set up an equation, draw a diagram, make a chart, or construct a table as a start to begin your problem-solving plan. Step 4: Check and Interpret: Check to see if you have used all your information. Solve Real- World Problems Using a Plan Example 1: Jeff is 10 years old. How old will Jeff be when he is twice as old as Ben? How many ears of corn will his crew harvest per hour? It will take 20 hours to harvest the entire field, so we need to divide 198,000 by 20 to get the number of ears picked per hour. Suppose Matthew's crew takes 36 hours to harvest the field. • Improper fractions are rational numbers where the numerator is greater than the denominator. A frog is sitting perfectly on top of number 7 on a number line. 93 Multi-Step Equations by Combining Like Terms In the last lesson, you learned the definition of like terms and how to combine such terms. This situation has several pieces of information: soda cans, slices of pizza, and party favors. 3p 4p 37 = 79 This equation requires three steps to solve. Use the Addition Property of Equality to get the variable on one side of the equal sign and the numerical values on the other. Apply the Addition Property of Equality: 7p 37 - 37 = 79 - 37. Apply the Multiplication Property of Equality: 7p 4- 7 = 42 -f 7. This lesson will show you how to use the Distributive Property to solve multi-step equations. Solution: Apply the Distributive Property: l Ox 18 = 78. Note that there is not always a match between the number of the practice exercise in the video and the number of the practice exercise listed in the following exercise set. " While this may seem weird to you, it is a true statement. 3x 2 -4y 2 x 4 Evaluate the expression: — — — ~[ x for x = -2, y 1. Note that there is not always a match between the number of the practice exercise in the video and the number of the practice exercise listed in the following exercise set. (3 7) -=-(7-12) 4 2-(3 (2-l)) (0 ~x 4 ' 4-(6 2) ^ °J 5. In this book, we will often use more than one method to solve a problem. You could draw a picture (it may take a while), write an equation, look for a pattern, or make a table. We need to figure out how many ears of corn are in the field. 198,000 20 9,900 The crew can harvest 9,900 ears per hour. Improper fractions can be rewritten as a mixed number - an integer plus a proper fraction. The frog jumps randomly to the left or right, but always jumps a distance of exactly 2. Evaluate the following expression: |d 7a 2 ; use a = (-1), d = 24. The length of a rectangle is one more inch than its width. We will use the following situation to further demonstrate solving equations involving like terms. You will need to provide 3 cans of soda per person, 4 slices of pizza per person, and 37 party favors. In general, to solve any equation you should follow this procedure. Remove any parentheses by using the Distributive Property or the Multiplication Property of Equality. Simplify each side of the equation by combining like terms. Apply the Addition Property of Equality: 10* 18 - 18 = 78 - 18. Apply the Multiplication Property of Equality: l Ox -f 10 = 60 4- 10. However, the practice exercise is the same in both.

.29 ounce ' 32 Arranging the rational numbers in ascending order: 0.0403125, 0.061875, 0.07375 Example 3: Which is greater | or |? Example: To prevent major accidents or injuries, these horses must be fenced in a rectangular pasture. The costs for each size areWhat could you use to quickly find out how much money you would earn for different hours of work? For example, sum, addition, more than, and plus all mean to add numbers together. Definition: To evaluate means to follow the verbs in the math sentence. To begin to evaluate a mathematical expression, you must first substitute a number for the variable. Solution: Evaluate means to follow the directions, which is to take 7 times y and subtract 11. When we have canceled all common factors, we have a fraction in its simplest form.

Example: What variables would be choices for the following situations? The following is a real-life example that shows the importance of evaluating a mathematical variable. Example 2: Cans of tomato sauce come in three sizes: 8 ounces, 16 ounces, and 32 ounces.

What could you use to quickly find out how much money you would earn for different hours of work? For example, sum, addition, more than, and plus all mean to add numbers together. Definition: To evaluate means to follow the verbs in the math sentence. To begin to evaluate a mathematical expression, you must first substitute a number for the variable. Solution: Evaluate means to follow the directions, which is to take 7 times y and subtract 11. When we have canceled all common factors, we have a fraction in its simplest form.

Example: What variables would be choices for the following situations? The following is a real-life example that shows the importance of evaluating a mathematical variable. Example 2: Cans of tomato sauce come in three sizes: 8 ounces, 16 ounces, and 32 ounces. $1.29 ounce ' 32 Arranging the rational numbers in ascending order: 0.0403125, 0.061875, 0.07375 Example 3: Which is greater | or |?

Example: To prevent major accidents or injuries, these horses must be fenced in a rectangular pasture. The costs for each size are $0.59, $0.99, and $1.29, respectively. Solution: Begin by creating a common denominator for these two fractions. 7 X 9 = 63, therefore the common denominator is 63.

Throughout this chapter, you will learn how to choose the best variables to describe a situation, simplify an expression using the Order of Operations, describe functions in various ways, write equations, and solve problems using a systematic approach. When someone is having trouble with algebra, they may say, "I don't speak math! You can also use a graphing calculator to evaluate expressions with more than one variable. Press [ENTER] to obtain the answer —.88 or _8 9" Practice Set Sample explanations for some of the practice exercises below are available by viewing the following video. When you are familiar with all of the problem-solving strategies, it is up to you to choose the methods that you are most comfortable with and that make sense to you. Set up an equation, draw a diagram, make a chart, or construct a table as a start to begin your problem-solving plan. Step 4: Check and Interpret: Check to see if you have used all your information. Solve Real- World Problems Using a Plan Example 1: Jeff is 10 years old. How old will Jeff be when he is twice as old as Ben? How many ears of corn will his crew harvest per hour? It will take 20 hours to harvest the entire field, so we need to divide 198,000 by 20 to get the number of ears picked per hour. Suppose Matthew's crew takes 36 hours to harvest the field. • Improper fractions are rational numbers where the numerator is greater than the denominator. A frog is sitting perfectly on top of number 7 on a number line. 93 Multi-Step Equations by Combining Like Terms In the last lesson, you learned the definition of like terms and how to combine such terms. This situation has several pieces of information: soda cans, slices of pizza, and party favors. 3p 4p 37 = 79 This equation requires three steps to solve. Use the Addition Property of Equality to get the variable on one side of the equal sign and the numerical values on the other. Apply the Addition Property of Equality: 7p 37 - 37 = 79 - 37. Apply the Multiplication Property of Equality: 7p 4- 7 = 42 -f 7. This lesson will show you how to use the Distributive Property to solve multi-step equations. Solution: Apply the Distributive Property: l Ox 18 = 78. Note that there is not always a match between the number of the practice exercise in the video and the number of the practice exercise listed in the following exercise set.

" While this may seem weird to you, it is a true statement. 3x 2 -4y 2 x 4 Evaluate the expression: — — — ~[ x for x = -2, y 1. Note that there is not always a match between the number of the practice exercise in the video and the number of the practice exercise listed in the following exercise set. (3 7) -=-(7-12) 4 2-(3 (2-l)) (0 ~x 4 ' 4-(6 2) ^ °J 5. In this book, we will often use more than one method to solve a problem. You could draw a picture (it may take a while), write an equation, look for a pattern, or make a table. We need to figure out how many ears of corn are in the field. 198,000 20 9,900 The crew can harvest 9,900 ears per hour. Improper fractions can be rewritten as a mixed number - an integer plus a proper fraction. The frog jumps randomly to the left or right, but always jumps a distance of exactly 2. Evaluate the following expression: |d 7a 2 ; use a = (-1), d = 24. The length of a rectangle is one more inch than its width. We will use the following situation to further demonstrate solving equations involving like terms. You will need to provide 3 cans of soda per person, 4 slices of pizza per person, and 37 party favors. In general, to solve any equation you should follow this procedure. Remove any parentheses by using the Distributive Property or the Multiplication Property of Equality. Simplify each side of the equation by combining like terms. Apply the Addition Property of Equality: 10* 18 - 18 = 78 - 18. Apply the Multiplication Property of Equality: l Ox -f 10 = 60 4- 10. However, the practice exercise is the same in both.

||What could you use to quickly find out how much money you would earn for different hours of work? For example, sum, addition, more than, and plus all mean to add numbers together. Definition: To evaluate means to follow the verbs in the math sentence. To begin to evaluate a mathematical expression, you must first substitute a number for the variable. Solution: Evaluate means to follow the directions, which is to take 7 times y and subtract 11. When we have canceled all common factors, we have a fraction in its simplest form. Example: What variables would be choices for the following situations? The following is a real-life example that shows the importance of evaluating a mathematical variable. Example 2: Cans of tomato sauce come in three sizes: 8 ounces, 16 ounces, and 32 ounces. $1.29 ounce ' 32 Arranging the rational numbers in ascending order: 0.0403125, 0.061875, 0.07375 Example 3: Which is greater | or |? Example: To prevent major accidents or injuries, these horses must be fenced in a rectangular pasture. The costs for each size are $0.59, $0.99, and $1.29, respectively. Solution: Begin by creating a common denominator for these two fractions. 7 X 9 = 63, therefore the common denominator is 63. Throughout this chapter, you will learn how to choose the best variables to describe a situation, simplify an expression using the Order of Operations, describe functions in various ways, write equations, and solve problems using a systematic approach. When someone is having trouble with algebra, they may say, "I don't speak math! You can also use a graphing calculator to evaluate expressions with more than one variable. Press [ENTER] to obtain the answer —.88 or _8 9" Practice Set Sample explanations for some of the practice exercises below are available by viewing the following video. When you are familiar with all of the problem-solving strategies, it is up to you to choose the methods that you are most comfortable with and that make sense to you. Set up an equation, draw a diagram, make a chart, or construct a table as a start to begin your problem-solving plan. Step 4: Check and Interpret: Check to see if you have used all your information. Solve Real- World Problems Using a Plan Example 1: Jeff is 10 years old. How old will Jeff be when he is twice as old as Ben? How many ears of corn will his crew harvest per hour? It will take 20 hours to harvest the entire field, so we need to divide 198,000 by 20 to get the number of ears picked per hour. Suppose Matthew's crew takes 36 hours to harvest the field. • Improper fractions are rational numbers where the numerator is greater than the denominator. A frog is sitting perfectly on top of number 7 on a number line. 93 Multi-Step Equations by Combining Like Terms In the last lesson, you learned the definition of like terms and how to combine such terms. This situation has several pieces of information: soda cans, slices of pizza, and party favors. 3p 4p 37 = 79 This equation requires three steps to solve. Use the Addition Property of Equality to get the variable on one side of the equal sign and the numerical values on the other. Apply the Addition Property of Equality: 7p 37 - 37 = 79 - 37. Apply the Multiplication Property of Equality: 7p 4- 7 = 42 -f 7. This lesson will show you how to use the Distributive Property to solve multi-step equations. Solution: Apply the Distributive Property: l Ox 18 = 78. Note that there is not always a match between the number of the practice exercise in the video and the number of the practice exercise listed in the following exercise set. " While this may seem weird to you, it is a true statement. 3x 2 -4y 2 x 4 Evaluate the expression: — — — ~[ x for x = -2, y 1. Note that there is not always a match between the number of the practice exercise in the video and the number of the practice exercise listed in the following exercise set. (3 7) -=-(7-12) 4 2-(3 (2-l)) (0 ~x 4 ' 4-(6 2) ^ °J 5. In this book, we will often use more than one method to solve a problem. You could draw a picture (it may take a while), write an equation, look for a pattern, or make a table. We need to figure out how many ears of corn are in the field. 198,000 20 9,900 The crew can harvest 9,900 ears per hour. Improper fractions can be rewritten as a mixed number - an integer plus a proper fraction. The frog jumps randomly to the left or right, but always jumps a distance of exactly 2. Evaluate the following expression: |d 7a 2 ; use a = (-1), d = 24. The length of a rectangle is one more inch than its width. We will use the following situation to further demonstrate solving equations involving like terms. You will need to provide 3 cans of soda per person, 4 slices of pizza per person, and 37 party favors. In general, to solve any equation you should follow this procedure. Remove any parentheses by using the Distributive Property or the Multiplication Property of Equality. Simplify each side of the equation by combining like terms. Apply the Addition Property of Equality: 10* 18 - 18 = 78 - 18. Apply the Multiplication Property of Equality: l Ox -f 10 = 60 4- 10. However, the practice exercise is the same in both.

.29 ounce ' 32 Arranging the rational numbers in ascending order: 0.0403125, 0.061875, 0.07375 Example 3: Which is greater | or |?Example: To prevent major accidents or injuries, these horses must be fenced in a rectangular pasture. The costs for each size are

Example: What variables would be choices for the following situations? The following is a real-life example that shows the importance of evaluating a mathematical variable. Example 2: Cans of tomato sauce come in three sizes: 8 ounces, 16 ounces, and 32 ounces.

Example: What variables would be choices for the following situations? The following is a real-life example that shows the importance of evaluating a mathematical variable. Example 2: Cans of tomato sauce come in three sizes: 8 ounces, 16 ounces, and 32 ounces. $1.29 ounce ' 32 Arranging the rational numbers in ascending order: 0.0403125, 0.061875, 0.07375 Example 3: Which is greater | or |?

Example: To prevent major accidents or injuries, these horses must be fenced in a rectangular pasture. The costs for each size are $0.59, $0.99, and $1.29, respectively. Solution: Begin by creating a common denominator for these two fractions. 7 X 9 = 63, therefore the common denominator is 63.

Throughout this chapter, you will learn how to choose the best variables to describe a situation, simplify an expression using the Order of Operations, describe functions in various ways, write equations, and solve problems using a systematic approach. When someone is having trouble with algebra, they may say, "I don't speak math! You can also use a graphing calculator to evaluate expressions with more than one variable. Press [ENTER] to obtain the answer —.88 or _8 9" Practice Set Sample explanations for some of the practice exercises below are available by viewing the following video. When you are familiar with all of the problem-solving strategies, it is up to you to choose the methods that you are most comfortable with and that make sense to you. Set up an equation, draw a diagram, make a chart, or construct a table as a start to begin your problem-solving plan. Step 4: Check and Interpret: Check to see if you have used all your information. Solve Real- World Problems Using a Plan Example 1: Jeff is 10 years old. How old will Jeff be when he is twice as old as Ben? How many ears of corn will his crew harvest per hour? It will take 20 hours to harvest the entire field, so we need to divide 198,000 by 20 to get the number of ears picked per hour. Suppose Matthew's crew takes 36 hours to harvest the field. • Improper fractions are rational numbers where the numerator is greater than the denominator. A frog is sitting perfectly on top of number 7 on a number line. 93 Multi-Step Equations by Combining Like Terms In the last lesson, you learned the definition of like terms and how to combine such terms. This situation has several pieces of information: soda cans, slices of pizza, and party favors. 3p 4p 37 = 79 This equation requires three steps to solve. Use the Addition Property of Equality to get the variable on one side of the equal sign and the numerical values on the other. Apply the Addition Property of Equality: 7p 37 - 37 = 79 - 37. Apply the Multiplication Property of Equality: 7p 4- 7 = 42 -f 7. This lesson will show you how to use the Distributive Property to solve multi-step equations. Solution: Apply the Distributive Property: l Ox 18 = 78. Note that there is not always a match between the number of the practice exercise in the video and the number of the practice exercise listed in the following exercise set.

" While this may seem weird to you, it is a true statement. 3x 2 -4y 2 x 4 Evaluate the expression: — — — ~[ x for x = -2, y 1. Note that there is not always a match between the number of the practice exercise in the video and the number of the practice exercise listed in the following exercise set. (3 7) -=-(7-12) 4 2-(3 (2-l)) (0 ~x 4 ' 4-(6 2) ^ °J 5. In this book, we will often use more than one method to solve a problem. You could draw a picture (it may take a while), write an equation, look for a pattern, or make a table. We need to figure out how many ears of corn are in the field. 198,000 20 9,900 The crew can harvest 9,900 ears per hour. Improper fractions can be rewritten as a mixed number - an integer plus a proper fraction. The frog jumps randomly to the left or right, but always jumps a distance of exactly 2. Evaluate the following expression: |d 7a 2 ; use a = (-1), d = 24. The length of a rectangle is one more inch than its width. We will use the following situation to further demonstrate solving equations involving like terms. You will need to provide 3 cans of soda per person, 4 slices of pizza per person, and 37 party favors. In general, to solve any equation you should follow this procedure. Remove any parentheses by using the Distributive Property or the Multiplication Property of Equality. Simplify each side of the equation by combining like terms. Apply the Addition Property of Equality: 10* 18 - 18 = 78 - 18. Apply the Multiplication Property of Equality: l Ox -f 10 = 60 4- 10. However, the practice exercise is the same in both.

||What could you use to quickly find out how much money you would earn for different hours of work? For example, sum, addition, more than, and plus all mean to add numbers together. Definition: To evaluate means to follow the verbs in the math sentence. To begin to evaluate a mathematical expression, you must first substitute a number for the variable. Solution: Evaluate means to follow the directions, which is to take 7 times y and subtract 11. When we have canceled all common factors, we have a fraction in its simplest form. Example: What variables would be choices for the following situations? The following is a real-life example that shows the importance of evaluating a mathematical variable. Example 2: Cans of tomato sauce come in three sizes: 8 ounces, 16 ounces, and 32 ounces. $1.29 ounce ' 32 Arranging the rational numbers in ascending order: 0.0403125, 0.061875, 0.07375 Example 3: Which is greater | or |? Example: To prevent major accidents or injuries, these horses must be fenced in a rectangular pasture. The costs for each size are $0.59, $0.99, and $1.29, respectively. Solution: Begin by creating a common denominator for these two fractions. 7 X 9 = 63, therefore the common denominator is 63. Throughout this chapter, you will learn how to choose the best variables to describe a situation, simplify an expression using the Order of Operations, describe functions in various ways, write equations, and solve problems using a systematic approach. When someone is having trouble with algebra, they may say, "I don't speak math! You can also use a graphing calculator to evaluate expressions with more than one variable. Press [ENTER] to obtain the answer —.88 or _8 9" Practice Set Sample explanations for some of the practice exercises below are available by viewing the following video. When you are familiar with all of the problem-solving strategies, it is up to you to choose the methods that you are most comfortable with and that make sense to you. Set up an equation, draw a diagram, make a chart, or construct a table as a start to begin your problem-solving plan. Step 4: Check and Interpret: Check to see if you have used all your information. Solve Real- World Problems Using a Plan Example 1: Jeff is 10 years old. How old will Jeff be when he is twice as old as Ben? How many ears of corn will his crew harvest per hour? It will take 20 hours to harvest the entire field, so we need to divide 198,000 by 20 to get the number of ears picked per hour. Suppose Matthew's crew takes 36 hours to harvest the field. • Improper fractions are rational numbers where the numerator is greater than the denominator. A frog is sitting perfectly on top of number 7 on a number line. 93 Multi-Step Equations by Combining Like Terms In the last lesson, you learned the definition of like terms and how to combine such terms. This situation has several pieces of information: soda cans, slices of pizza, and party favors. 3p 4p 37 = 79 This equation requires three steps to solve. Use the Addition Property of Equality to get the variable on one side of the equal sign and the numerical values on the other. Apply the Addition Property of Equality: 7p 37 - 37 = 79 - 37. Apply the Multiplication Property of Equality: 7p 4- 7 = 42 -f 7. This lesson will show you how to use the Distributive Property to solve multi-step equations. Solution: Apply the Distributive Property: l Ox 18 = 78. Note that there is not always a match between the number of the practice exercise in the video and the number of the practice exercise listed in the following exercise set. " While this may seem weird to you, it is a true statement. 3x 2 -4y 2 x 4 Evaluate the expression: — — — ~[ x for x = -2, y 1. Note that there is not always a match between the number of the practice exercise in the video and the number of the practice exercise listed in the following exercise set. (3 7) -=-(7-12) 4 2-(3 (2-l)) (0 ~x 4 ' 4-(6 2) ^ °J 5. In this book, we will often use more than one method to solve a problem. You could draw a picture (it may take a while), write an equation, look for a pattern, or make a table. We need to figure out how many ears of corn are in the field. 198,000 20 9,900 The crew can harvest 9,900 ears per hour. Improper fractions can be rewritten as a mixed number - an integer plus a proper fraction. The frog jumps randomly to the left or right, but always jumps a distance of exactly 2. Evaluate the following expression: |d 7a 2 ; use a = (-1), d = 24. The length of a rectangle is one more inch than its width. We will use the following situation to further demonstrate solving equations involving like terms. You will need to provide 3 cans of soda per person, 4 slices of pizza per person, and 37 party favors. In general, to solve any equation you should follow this procedure. Remove any parentheses by using the Distributive Property or the Multiplication Property of Equality. Simplify each side of the equation by combining like terms. Apply the Addition Property of Equality: 10* 18 - 18 = 78 - 18. Apply the Multiplication Property of Equality: l Ox -f 10 = 60 4- 10. However, the practice exercise is the same in both.

.29 ounce ' 32 Arranging the rational numbers in ascending order: 0.0403125, 0.061875, 0.07375 Example 3: Which is greater | or |?Example: To prevent major accidents or injuries, these horses must be fenced in a rectangular pasture. The costs for each size are [[