S E S N Writing Expressions and Equations Goal: Write variable expressions and equations. Vocabulary Verbal model: EXAMPE 1 Translating Verbal Phrases Verbal phrase Expression a. A number increased by b. 9 less than a number c. 1 more than three times a number d. 5 decreased by the quotient of a number and When translating verbal sentences into equations, look for the key words "is" and "equals," which can be represented by the symbol =. EXAMPE Translating Verbal Sentences Verbal sentence a. 1 increased by a number is 18. b. The difference of a number and 6 equals. Equation c. The product of and a number is 15. d. is equal to five times the sum of a number and. esson 7.1 Writing Expressions and Equations 1
Guided Practice Write the verbal phrase or sentence as a variable expression or equation. et n represent the number. 1. 9 added to a number. 1 of a number increased by 18. divided by a number equals 6.. 6 minus times a number is 10. EXAMPE Writing and Solving an Equation Dinner The cost of a fish dinner is times the cost of a chef salad. The fish dinner costs $1. Find the cost of the chef salad. Assign a meaningful variable to represent what you need to find. In Example, s is chosen to represent the price of a salad. Solution Write a verbal model. et s represent the cost of the salad. times the cost of a Cost of a Use mental math: Because times is 1, s. Answer: The cost of a chef salad is $. Guided Practice Use mental math to solve the following problem. 5. This year, the enrollment at the local junior college dropped by 500 to 50. Write and solve an equation to find the enrollment last year. 1 Chapter 7 Notetaking Guide
E SSN 7.1 Name Practice B For use with pages 7 1 Date esson 7.1 Write the verbal phrase as a variable expression. et x represent the number. 1. A number added to 10. 1 decreased by a number. times a number. 1 increased by a number 5. 11 decreased by the quotient of 9 and a number 6. Twice a number subtracted from 1 Write the verbal sentence as an equation. et y represent the number. 7. 15 increased by a number equals 7. 8. The difference of a number and is 19. 9. The sum of twice a number and 7 is. 10. 1 of a number decreased by 1 equals 5. Write a verbal phrase for the variable expression. 11. x 1 1. 9 a 1. m 5 Write a verbal sentence for the equation. 1. b 7 15. 8y 7 16. 11 x 0 Write the real-world phrase as a variable expression. Be sure to identify what the variable represents. 17. 1 mile more than yesterday s run 18. Two times your previous high score 19. ne-third of the recipe 0. inches shorter than your other dog 1. Yosemite National Park has many natural waterfalls within its boundaries, including Horsetail Fall and Yosemite Falls. Horsetail Fall, which is 1000 feet tall, is 15 feet shorter than Yosemite Falls. Write an equation to find the height of Yosemite Falls. Then use mental math to solve the equation.. The population of Cape Coral, Florida increased by 7 thousand people from 1990 to 000. In 000, the population of Cape Coral was 10 thousand people. Write an equation to find the population of Cape Coral in 1990. Then use mental math to solve the equation.. In 001, the cost of mailing a letter was 17 times the cost of mailing a letter in 1885. If it cost $. to mail a letter in 001, find the cost of mailing a letter in 1885. 6 McDougal ittell Math, Course Chapter 7 Resource Book Copyright McDougal ittell/houghton Mifflin Company All rights reserved.
E SSN 7.1 Name Practice C For use with pages 7 1 Date Write the verbal phrase as a variable expression. et x represent the number. 1. The sum of 8 and twice a number. of a number decreased by 1. 8 increased by the quotient of 1 and a number Write the verbal sentence as an equation. et y represent the number.. The difference of and a number equals 15. 5. The sum of twice a number and 1 is 8. esson 7.1 6. of a number decreased by is. Write a verbal phrase for the variable expression. 7. 5 y 8. b 1 9. 5 n Write a verbal sentence for the equation. 10. a 6 1 11. 7 x 15 1. 1 x 8 Write the real-world phrase as a variable expression. Be sure to identify what the variable represents. 1. 1 minutes longer than last week s run 1. Three-quarters of the total time 15. times higher than your previous score 16. 1 inches shorter than your other dog 17. The population of Alexandria, Virginia increased by 17 thousand people from 1990 to 000. In 000, the population of Alexandria was 18 thousand people. Write an equation to find the population of Alexandria in 1990. Then use mental math to solve the equation. 18. In 000, the number of visitors to Cuyahoga Valley National Park 1 in hio was about of the total number of visitors to all national 0 parks in the United States. If 00 thousand people visited Cuyahoga National Park in 000, find the total number of visitors to all national parks in the United States in 000. 19. Describe a real-world situation that can be represented by the expression x 8. 0. You rent two movies from a video store for $6.95 each and g video games for $.95 each. You have $5 to spend on the movies and the video games. Write an equation that represents the situation. Copyright McDougal ittell/houghton Mifflin Company All rights reserved. McDougal ittell Math, Course 7 Chapter 7 Resource Book
S E S N Simplifying Expressions Goal: Simplify variable expressions. Vocabulary Term: ike terms: Equivalent variable expressions: Coefficient: Constant term: EXAMPE 1 Combining ike Terms Simplify the expression 8x x. After Example 1, the step of using the distributive property in order to combine like terms will not be shown. 8x x 8x Write expression as a sum. Commutative property of addition Distributive property Simplify. Rewrite without parentheses. esson 7. Simplifying Expressions 15
EXAMPE Coefficients, Constant Terms, ike Terms Identify the coefficients, constant terms, and like terms of the expression x 7 x 1. First, write the expression as a sum: x x. Coefficient is. Coefficient is. x x and and are like terms. are like terms. EXAMPE Simplifying an Expression Simplify the expression (m 1) 6. (m 1) 6 Distributive property Write as a sum. Combine like terms. Guided Practice Identify the coefficients, constant term(s), and like terms of the expression. Then simplify the expression. 1. n n. 10 6p 5p. l 9 l 6 16 Chapter 7 Notetaking Guide
EXAMPE Writing and Simplifying an Expression Construction A rectangular skylight in an office building is times as long as it is wide. Write and simplify an expression for the perimeter of the skylight in terms of the width w. Solution Because the skylight is times as long as it is wide, its length is. Perimeter l w Formula for perimeter of a rectangle w Substitute for l. w Multiply. Combine like terms. Answer: An expression for the perimeter of the skylight is. Guided Practice Complete the following exercise.. A rectangle is inches longer than it is wide. Write and simplify an expression for the perimeter of the rectangle in terms of the width w. esson 7. Simplifying Expressions 17
E SSN 7. Name Practice B For use with pages 5 Date Tell whether the statement is true or false. 1. The coefficients of the expression 8 5x x are 5 and.. The constants of the expression 11x 9 8x are and 9.. In the expression x 9 10x, x and are like terms.. The expressions 15x 9 x and 11x 7 are equivalent. Identify the coefficients, constant term(s), and like terms of the expression. 5. 8x 9 x 6. 17 a 5a 1 7. 7m 7 6m 6 8. 10 15r r 8 esson 7. Match the expression with an equivalent expression. 9. 5x x 9 A. x 10. 5(x ) x 7 B. x 5 11. 5x 6 7x 9 C. x 8 Simplify the expression. 1. 18n 1 5n 1. x 6 9x 1 1. 1a 7 a 7 15. 6 1r 1r 16. (5 b) 17. 6( z) 11z 18. A nut mixture contains peanuts, walnuts, and cashews. In the mixture, the amount of peanuts is three times the amount of cashews, and the amount of walnuts is four times the amount of cashews. et x represent the amount of cashews. Write and simplify an expression for the total amount of nuts in the mixture. 19. A rectangular sheet of plywood is seven times longer than it is wide. Write and simplify an expression for the perimeter of the rectangle in terms of the width w. 0. A basketball player scored 8 points total during the first and second quarters of a game. During the third quarter, she scored three times as many points as she did in the fourth quarter. et x represent the number of points the player scored in the fourth quarter. Write and simplify an expression to represent the total number of points the player scored during the entire game. 16 McDougal ittell Math, Course Chapter 7 Resource Book Copyright McDougal ittell/houghton Mifflin Company All rights reserved.
E SSN 7. Name Practice C For use with pages 5 Date Identify the coefficients, constant term(s), and like terms of the expression. 1. 19 x 7x 1. 10a 10 8a 8. 1 9m 5m 6. w 1w 1 5. 5(z 6) z 6. (b ) 7 Write and simplify an expression for the perimeter of the rectangle. 7. 8. 9. x 7a m 1 x 9 5a 7m Simplify the expression. 10. 18s 1s 7 11. 9 17a 1a 1. 1 1x 5x 1 1. ( y 6) 1 1. (b 7) 1b 8 15. 6(5 t) 17 5t 16. (w z) w z 6 17. 6(r s) (r s) esson 7. 18. A nut mixture contains peanuts, walnuts, and cashews. In the mixture, the amount of peanuts is four times the amount of cashews, and the amount of walnuts is 1 1 times the amount of cashews. et x represent the amount of cashews. Write and simplify an expression for the total amount of nuts in the mixture. 19. A rectangular sheet of plywood is eight times longer than it is wide. Write and simplify an expression for the perimeter of the rectangle in terms of the width w. 0. A basketball player scored 1 as many points in the second quarter than she scored during the first quarter. During the third quarter, she scored three times as many points as she did in the fourth quarter. Write and simplify an expression to represent the total number of points the player scored during the entire game. Tell whether the two expressions are equivalent. 1. 9 10x 1;. 18c 9c 1;. 7y y; 6x x (c ) 11y Copyright McDougal ittell/houghton Mifflin Company All rights reserved. McDougal ittell Math, Course 17 Chapter 7 Resource Book
E S S N Solving Addition and Subtraction Equations Goal: Solve addition and subtraction equations. Vocabulary Inverse operations: Equivalent equations: Subtraction Property of Equality Words Subtracting the same number from each side of an equation produces an Algebra x a b equation. x a a b EXAMPE 1 Solving an Addition Equation Solve x 1. x 1 Write original equation. from each side. Simplify. Check x 1 Write original equation. Substitute for x. Solution checks. 18 Chapter 7 Notetaking Guide
Addition Property of Equality Words Adding the same number to each side of an equation produces an equation. Algebra x a b x a a b EXAMPE Solving a Subtraction Equation WATCH UT! You can add or subtract vertically or horizontally to solve equations, but remember to perform the same operation on each side of the equation. Solve y 9. y 9 Write original equation. to each side. Simplify. Check y 9 Write original equation. Substitute for y. Solution checks. EXAMPE Combining ike Terms Solve 7.1 b 1. 7.1 b 1 Write original equation..1 Commutative property of addition Combine like terms. from each side. Simplify. Check 7.1 b 1 Write original equation. Substitute for b. Solution checks. esson 7. Solving Addition and Subtraction Equations 19
Guided Practice Solve the equation. Check your solution. 1. t 7 1. n 8 0. 6 y. r 1 15 5. p (.6).9 6..7 s 1.9 5. EXAMPE Writing and Solving an Equation Business Travel Carol is out of the office for 8 hours meeting with a client. She spends 0.75 hour driving to the client s office, and 1.5 hours driving back from the client s office. How long was Carol at the client s office? Solution Write a verbal model. et h represent the number of hours Carol spent at the client s office. Time away from office Write equation. Combine like terms. from each side. Simplify. Answer: Carol spent hours at the client s office. 150 Chapter 7 Notetaking Guide
E SSN 7. Name Practice B For use with pages 6 5 Date Tell whether the given value of the variable is a solution of the equation. 1. x 15 0; x 5. a 1 1; a 1. 7 m 1; m Solve the equation. Check your answer.. y 6 15 5. n 1 6. 18 r 7 7. a 1 8 8. z 9 9. 0 s 5 10..6 m.5 11. c.1 6.7 1.. x 1. 7.5 1. t 1 5 1. 6 10 7 a 1 15. 1 x 5 6 16. Describe and correct the error in solving the equation 1.8 a.5. Write the verbal sentence as an equation. Then solve the equation. 17. The difference of a number b and 8 is 15. 18. 9 more than a number x is. 1.8 a.5 1.8 a 1.8.5 1.8 a.7 Write and solve an equation to find the unknown side length. 19. Perimeter: 1 ft 0. Perimeter: 11. mm 1. Perimeter: 1. in. esson 7. ft? ft 1.8 mm? 5 mm 1. mm.9 in..6 in.?.7 in.. A paperback version of a book costs $17.10. This cost is $.89 less than the cost of the hardcover version of the book. Write and solve an equation to find the hardcover cost of the book.. During a recent trip to the gym, you worked out with free weights and rode a stationary bike. You used a stationary bike for 8 minutes of the 75 minutes you spent at the gym. Write and solve an equation to find the number of minutes you spent working out with free weights.. The left- and right-hand margins on a sheet of paper are both 1.5 inches wide. The total width of the sheet of paper is 8.5 inches. Write and solve an equation to find the width of the text area that lies between the margins. 6 McDougal ittell Math, Course Chapter 7 Resource Book Copyright McDougal ittell/houghton Mifflin Company All rights reserved.
E SSN 7. Name Practice C For use with pages 6 5 Date Solve the equation. Check your answer. 1. y 9 1. a 15 8. m 0.5..6 r. 5. 7.6 q 8.1 5 6. b 1. 9.8 7. 9.6 w.5 8 8. 6. t t 9. 6.8 p 9.5 7. 10. 6x 5x 5 7 11. n 8 1. x 1 5 Write the verbal sentence as an equation. Then solve the equation. 1. The difference of a number n and 1 is.6. 1..5 less than a number w is 1. 15. 5. more than a number b is. 16. The sum of 0.8 and a number z is.. 17. A number y decreased by 1 is 5. 18. increased by a number n is 1. Write and solve an equation to find the unknown side length. 19. Perimeter: ft 0. Perimeter: 0 mm 1. Perimeter:.9 in. 6 ft? 8 ft.1 mm? 8. mm.9 mm 0.8 in. 0.5 in.? 1. in.. A paperback version of a book costs $19.95. This cost is $1.61 less than the cost of the hardcover version of the book. Write and solve an equation to find the hardcover cost of the book.. During a recent trip to the gym, you worked out with free weights and ran on the track. You ran on the track for 8 minutes of the 95 minutes you spent at the gym. Write and solve an equation to find the number of minutes you spent working out with free weights. esson 7.. The left- and right-hand margins on a sheet of paper are both 0.75 inch wide. The total width of the sheet of paper is 8.5 inches. Write and solve an equation to find the width of the text area that lies between the margins. 5. Solve the equation 1 5 7 9 8m 9m. 7 6. Write an addition equation and a subtraction equation that both have a solution of 5. Copyright McDougal ittell/houghton Mifflin Company All rights reserved. McDougal ittell Math, Course 7 Chapter 7 Resource Book
S E S N Solving Multiplication and Division Equations Goal: Solve multiplication and division equations. Division Property of Equality Words Dividing each side of an equation by the same nonzero number produces an equation. Algebra ax b (a 0) a x a EXAMPE 1 Solving a Multiplication Equation Solve 0 6x. 0 6x 0 6x Write original equation. Simplify. each side by. Check 0 6x Write original equation. Substitute for x. Solution checks. Multiplication Property of Equality Words Multiplying each side of an equation by the same nonzero number produces an equation. Algebra a x b (a 0) a p a x esson 7. Solving Multiplication and Division Equations 151
In your notebook, you may want to compare and contrast solving mulitiplication and division equations. This will help you remember how to solve these types of equations. EXAMPE Solving a Division Equation Solve x 0.. x 0. Write original equation. each side by. Simplify. EXAMPE Solving an Equation Using a Reciprocal Need help with multiplying by a reciprocal? See page 7 of your textbook. Solve x 6. x 6 Write original equation. each side by. Simplify. Guided Practice Solve the equation. Check your solution. 1. 9v 6. 8b 96. 1.7 k. d 15 15 Chapter 7 Notetaking Guide
5. 6q q 16 6. 5 m 10 8 EXAMPE Standardized Test Practice Rollerblading A woman is rollerblading through the park. You measure a 75-foot stretch of sidewalk, and count that she skates that portion of the sidewalk in 1 seconds. What is the speed of the woman? A 65 feet per second B feet per second C 6.5 feet per second D 50 feet per second Solution Use the formula d rt. d rt Write formula for distance. Substitute for d and for t. each side by. Simplify. Answer: The speed of the woman is feet per second. The correct answer is. A B C D Guided Practice Solve the following problem. 7. A filmmaker makes an edited version of his movie that is 10 minutes long. The unedited footage is 7 times as long as the edited version. Write and solve an equation to find the length of the unedited film. esson 7. Solving Multiplication and Division Equations 15
E SSN 7. Name Practice B For use with pages 5 60 Date Tell whether the given value of the variable is a solution of the equation. n 1. 5r 15; r 15..a 1; a 5. 8; n 1 6 Describe how to solve the equation without actually solving. m. 8x 7 5. 1b 8 6. 6 1 1 Solve the equation. Check your solution. Round the solution to the nearest hundredth if necessary. 7. p 8 8..y 0.7 9. 5 1 c 5 10. 9d 76.5 11. m 7 1. z.5 6. a w 1..6 1. 9.8 15. 6 8. 8 r 16. 5 t 0 17. 5.q 1.1 18. b b 8 Write the verbal sentence as an equation. Then solve the equation. 19. The quotient of a number x and 6 is 8.7. 0. Three times a number a equals 1.. 1. The product of. and a number m is 1... At a part-time job, Marcus earns $8.50 per hour. Write and solve an equation to find the number of hours he has to work to earn $10.. It costs you $1.96 for four pounds of bananas. Write and solve an equation to find the cost of one pound of bananas.. In a survey about favorite book categories, 1 of the total number of people surveyed, or 9 people, responded that mystery was their favorite category. Write and solve an equation to find the total number of people surveyed. esson 7. Copyright McDougal ittell/houghton Mifflin Company All rights reserved. McDougal ittell Math, Course 7 Chapter 7 Resource Book
E SSN 7. Name Practice C For use with pages 5 60 Date Describe how to solve the equation without actually solving. b 1. 9x 7. 9 1 Solve the equation. Check your solution. Round the solution to the nearest hundredth if necessary.. 8 m. 5.y 1.6 5. c 6. 8d 9.6 5 7. m 7 51 8. z. 8.7 9. a.5 6 w 10. 5. 11. 8 7.1 9 r 1. 7 t 1 1..6q 1.87 1. b 7b 9 15. 1 7p 9p Write the verbal sentence as an equation. Then solve the equation. 16. The quotient of a number y and 7 is.9. 17. of a number n is equal to 150. 18. The product of 1.7 and a number s is 1.6. 19. At a part-time job, Sheila works.5 hours a week. Write and solve an equation to find the amount of money she gets paid in one hour if she earns $07 for the.5 hours of work. 0. It costs you $.50 for.5 pounds of cheese. Write and solve an equation to find the cost of one pound of cheese. 1. In a survey about favorite book categories, of the total number of people surveyed, or 6 people, responded that fiction was their favorite category. Write and solve an equation to find the total number of people surveyed.. Which two equations have the same solution? Explain your reasoning. x 1 A. 17 B. 17x 8 C. 8x 1 D. 0.15x 17 8 7 esson 7. 8 McDougal ittell Math, Course Chapter 7 Resource Book Copyright McDougal ittell/houghton Mifflin Company All rights reserved.
E S S N Solving Two-Step Equations Goal: Solve two-step equations. EXAMPE 1 Solving a Two-Step Equation Solve m 7 19. m 7 19 Write original equation. Simplify. to each side. Don't forget to check your solution by substituting back into the original equation. each side by. Simplify. EXAMPE Solving a Two-Step Equation p Solve 7. 5 p 7 Write original equation. 5 from each side. Simplify. each side by. Simplify. 15 Chapter 7 Notetaking Guide
Guided Practice Solve the equation. Check your solution. 1. 7q 10. 6 j 0. 5 y 6 6 EXAMPE Writing and Solving a Two-Step Equation ong Distance Calls A long distance phone company charges customers a $5 monthly fee plus $ per hour for long distance phone calls. ne customer s bill was $. How many hours of long distance calls did the customer make? Solution Write a verbal model. et h represent the number of hours of long distance the customer used. Monthly Hourly cost of Hours of p Total cost fee long distance long distance p Write equation. Simplify. from each side. each side by. Simplify. Answer: The customer made hours of long distance phone calls. esson 7.5 Solving Two-Step Equations 155
E SSN 7.5 Name Practice B For use with pages 61 65 Date esson 7.5 Tell whether the given value of the variable is a solution of the equation. 1. 6x 5 1; x. 8m 7 17; m. c 1 ; c 1 Match the equation with its solution.. y 1 A. y 1 5. y 1 B. y 1 6. y 1 C. y 1 7. y 1 D. y 1 8. Put the steps for solving the equation 9x 8 5 in order. A. Divide each side by 9. B. Write original equation. C. Check your answer. D. Add 8 to each side. Solve the equation. Check your solution. 9. 7a 17 10. 5s 1 68 11. 1 x 19 1. n 6 1. d. 6 1 1. 1 p 7 7 15. 0 1t 6 16. m 5 16 17..c 1.7 6.8 Write the verbal sentence as an equation. Then solve the equation. 18. Twice the number r increased by 15 equals 17. 19. 8 subtracted from times a number c is 1. 0. A mail-order CD company is advertising a sale. During the sale, CDs are $6.95 each and the shipping and handling charge is only $5.5. How many CDs can you buy for $0? 1. A window is 1 inches wide, and its perimeter is 11 inches. What is the length of the window?. Kathy earns $5 a week for 0 hours of work and $5 an hour for each hour over 0. How many hours did Kathy work if she earned $570 in one week? Copyright McDougal ittell/houghton Mifflin Company All rights reserved. McDougal ittell Math, Course 7 Chapter 7 Resource Book
esson 7.5 E SSN 7.5 Name Practice C For use with pages 61 65 Date Describe the steps to solve the equation. Do not solve. 1 1. 11x 7 1. y 10 8 Solve the equation. Check your solution.. 8a 5 7. 6s 1 56 5. 8 7x n 6..5 7 8 7. d 5.8 1 11. 8. 1 p 5 8 9. 0 18t 10. m 7 19 11..c 7.1 1. 1. (x 5) 8 1. b 1 1. 9 7x 5 9 Write the verbal sentence as an equation. Then solve the equation. 15. 5 of a number b increased by 18 equals. 6 16. 9 subtracted from times a number t is. 17. A mail-order CD company is advertising a sale. During the sale, CDs are $7.95 each and the shipping and handling charge is only $.5. How many CDs can you buy for $60? 18. A door is 6 inches wide, and its perimeter is 0 inches. What is the length of the door? 19. Frank earns $75 a week for 0 hours of work and $8 an hour for each hour over 0. How many hours did Frank work if he earned $601 in one week? 0. n the first three 100-point tests of the grading period, your scores were 88, 91, and 7. What score do you need to get on the fourth 100-point test to have a mean of 86? 1. Write a two-step equation whose solution is.. Explain why you should check your answer after solving an equation. 8 McDougal ittell Math, Course Chapter 7 Resource Book Copyright McDougal ittell/houghton Mifflin Company All rights reserved.
E S S N Solving Inequalities Goal: Write and solve inequalities. Vocabulary Inequality: Solution of an inequality: Graph of an inequality: Equivalent inequalities: EXAMPE 1 Graphing Inequalities The inequality symbol is read "is less than or equal to." The inequality symbol is read "is greater than or equal to." Inequality Verbal phrase Graph a. x < All numbers b. x All numbers or 5 1 0 1 5 5 1 0 1 5 c. x > All numbers 5 1 0 1 5 d. x 1 All numbers or 1 5 1 0 1 5 156 Chapter 7 Notetaking Guide
EXAMPE Solving an Inequality Solve f 1. Then graph the solution. f 1 Write original inequality. to each side. Simplify. To graph, use a(n) dot and draw the arrow pointing to the. 1 0 1 5 6 Check To check the solution, choose any number to substitute for f. Use f 1 in the check below. f 1 Write original inequality.? 1 Substitute for f. 1 Solution checks. Guided Practice Solve the inequality. Then graph the solution. 1. s 1. < b. w 1 > 1 5 6 7 8 5 6 7 8 9 10 5 1 0 1 esson 7.6 Solving Inequalities 157
EXAMPE Solving an Inequality Solve m < 1. Then graph the solution. WATCH UT! Don t forget to reverse the inequality when you multiply or divide each side of an inequality by a negative number. m < 1 Write original inequality. each side by. inequality. Simplify. To graph, use a(n) dot and draw the arrow pointing to the. 0 1 5 6 7 8 Guided Practice Solve the inequality. Then graph the solution.. x 1 5. 5s < 0 6. n 10 1 5 6 7 9 8 7 6 5 7 8 9 10 11 1 1 158 Chapter 7 Notetaking Guide
E SSN 7.6 Name Practice B For use with pages 66 70 Date Tell whether the given value of the variable is a solution of the inequality. 1. x 7 5; x 8. a 6; a 9. m < ; m Write an inequality represented by the graph.. 5. 1 0 1 5 6 7 6. 7. 9 6 0 6 9 1 15 6 5 1 0 1 1 0 1 esson 7.6 8. Describe and correct the error in finding the solution to 8p 7. 8p 7 8 p 7 8 8 p 7 8 Write an inequality to represent the situation. Then graph the inequality. 9. To ride an amusement park ride, you must be 8 inches tall or taller. 10. A restaurant can hold at most 0 people. 11. To run for the President of the United States, you must be at least 5 years old. Solve the inequality. Then graph the solution. 1. x 8 < 15 1. c 1 8 1. m 0 15. 1 r > 16. 6 w 10 17. 5a < 0 x 1 18. 8 19. n > 15 1. A wheelbarrow can carry at most 00 pounds. Write and solve an inequality to find the greatest number of 50-pound bags of concrete that the wheelbarrow can carry.. A book store sells used paperbacks for $.75 each. You receive a $ discount if you spend at least $0 in the store. Write and solve an inequality that represents the least number of paperbacks you must buy in order to receive the discount. Copyright McDougal ittell/houghton Mifflin Company All rights reserved. 0. q < 18. You are mailing a -pound item by parcel post. The total weight of an item and its packaging cannot be greater than 70 pounds. Write and solve an inequality that represents the heaviest the packaging can be without exceeding the 70-pound weight limit. McDougal ittell Math, Course 57 Chapter 7 Resource Book
E SSN 7.6 Name Practice C For use with pages 66 70 Date Tell whether the given value of the variable is a solution of the inequality. 1. 1 x ; x 1. a < 8; a. m 1 ; m esson 7.6 Write an inequality represented by the graph.. 5. 0 1 5 6 7 8 6. 7. 1510 5 0 5 10 15 0 5 5 1 0 1 9 8 7 6 5 1 Write an inequality to represent the situation. Then graph the inequality. 8. To ride an amusement park ride, you must be 5 inches tall or taller. 9. A restaurant can hold at most 5 people. 10. In most states, you must be at least 16 years old to drive a motor vehicle. Solve the inequality. Then graph the solution. x 11. 17 r > 51 1. 65 w 1 1. 8 x n 1. > 8 15. 1 8 6 16. q 18 5 17. 11a < 18. x < 5 19. 7x 16 0. A wheelbarrow can carry at most 500 pounds. Write and solve an inequality to find the greatest number of 0-pound bags of concrete that the wheelbarrow can carry. 1. A book store sells used paperbacks for $.75 each. You receive a $ discount if you spend at least $6 in the store. Write and solve an inequality that represents the least number of paperbacks you must buy in order to receive the discount.. You are mailing a 5-pound item and a 7-pound item in the same package by parcel post. The total weight of the items and their packaging cannot be greater than 70 pounds. Write and solve an inequality that represents the heaviest the packaging can be without exceeding the 70-pound weight limit.. Write a two-step inequality whose solution is x <. 58 McDougal ittell Math, Course Chapter 7 Resource Book Copyright McDougal ittell/houghton Mifflin Company All rights reserved.
S E S N Functions and Equations Goal: Write and evaluate function rules. Vocabulary Function: Input: utput: Domain: Range: EXAMPE 1 Evaluating a Function Evaluate the function y x when x 8. y x Write rule for function. Substitute for x. Multiply. esson 7.7 Functions and Equations 159
EXAMPE Making an Input-utput Table Make an input-output table for the function y x. using the domain 0, 1,, and. Then state the range of the function. Solution Input x 0 1 Substitution y. y. y. y. utput y The range of the function is the set of outputs:,,, and. Guided Practice Complete the following exercise. 1. Make an input-output table for the function y x using the domain, 1, 0, 1, and. Then state the range of the function. EXAMPE Writing a Function Rule Write a function rule for the input-output table. Input x 1 0 1 utput y.5.5 1.5 0.5 0.5 1.5.5 Solution You can see that you obtain each output by the input. Answer: The function rule given by the table is. 160 Chapter 7 Notetaking Guide
EXAMPE Writing a Function Rule From a Pattern Squares In the diagram of the squares, the input s is the length of each side of a square. The output P is the perimeter of the square. Write a rule for the function. Then use the rule to find the perimeter of a square with sides 9 units. 1 unit units units units Solution 1. Begin by making an input-output table. Input utput. Notice that each output value is the input value. So, a rule for the function is.. To find the perimeter of a square with sides 9 units, evaluate the function when s 9. Because P, the perimeter of the square is. Guided Practice Write a function rule for the input-output table... Input x 1 0 1 Input x 6 8 utput y 0 utput y 1 1 11 esson 7.7 Functions and Equations 161
E SSN 7.7 Name Practice B For use with pages 71 75 Date Evaluate the function y 5x for the given value of x. 1. 7. 0. Match the function with its possible range.. y x 1 A. 7,, 1,, 5, 8 5. y x B. 5,, 1, 1, 6. y x 1 C. 11, 6, 1,, 9, 1 7. y 5x 1 D.,,, 1, 0 Make an input-output table for the function using the domain, 1, 0, 1, and. Then state the range of the function. 8. y x 8 9. y 15x 10. y.x 11. y x.75 1. y 0.x 1. y 18 x esson 7.7 Write a function rule for the input-output table. 1. Input x 0 1 15. utput y 5 6 16. Input x 1 0 17. utput y 1 8 0 Input x 0 1 utput y 5 Input x 0 1 utput y 1.... 18. A custom case company makes travel cases for computer equipment. There is a -inch foam lining around the inside of each case. The function y x, where x is the width of a laptop computer, can be used to find the total width of a laptop case, including the foam lining. Create an input-output table using the domain 1, 15, 18, and 1. foam computer x in. in. in. 19. A magazine costs $.95 per issue. Write a function rule that models the cost y of x issues. Then use the function to calculate the cost of 6 issues. 0. It costs $.15 to make one copy on the copier at the local library. Write a function rule that models the cost y of making x copies. Then use the function to calculate the cost of copies. 68 McDougal ittell Math, Course Chapter 7 Resource Book Copyright McDougal ittell/houghton Mifflin Company All rights reserved.
E SSN 7.7 Name Practice C For use with pages 71 75 Date Evaluate the function y 5.x for the given value of x. 1. 8. 0. 7 Make an input-output table for the function using the domain, 1, 0, 1, and. Then state the range of the function.. y x 1 5. y x 6. y 7.x 7. y x 9.85 8. y 1.x 9. y 1 x Write a function rule for the input-output table. 10. Input x 1 0 1 11. utput y 7 6 5 Input x 5 utput y 0. 1... 1. Input x 5 6 7 1. Input x 0 1 utput y 55 66 77 utput y 1.6.6.6.6 Write a function rule for the points in the coordinate plane. 1. y 15. y 16. 6 5 7 6 5 1 1 x 1 1 x 8 1 y 1 x esson 7.7 17. A magazine costs $.95 per issue. Write a function rule that models the cost y of x issues. Then use the function to calculate the cost of 1 issues. 18. A custom case company makes travel cases for computer equipment. There is a.5-inch foam lining around the inside of each case. Write a function rule that represents the total width y of the case in terms of the width x of a laptop computer. Then find the width of a case for a 15-inch wide laptop. 19. Write two different functions for which an input of 5 gives an output of 8. foam computer x in..5 in..5 in. Copyright McDougal ittell/houghton Mifflin Company All rights reserved. McDougal ittell Math, Course 69 Chapter 7 Resource Book
E S S N Graphing Functions Goal: Graph functions in a coordinate plane. Vocabulary inear function: EXAMPE 1 Graphing a Function Graph the function y x 1. When the domain of a function is not given, assume that it includes every x-value for which the function can produce a corresponding y-value. 1. Make an input-output table by choosing several input values and evaluating the function for the output values.. Use the table to write a list of ordered pairs: x Substitution y 1 0 1. Plot the ordered pairs in a coordinate plane.. Notice that all of the points lie on a line. Any other ordered pairs satisfying y x 1 would also lie on the line when graphed. The line represents the complete graph of the function y x 1. 7 6 5 7 6 5 1 5 6 7 y 1 5 6 7 x 16 Chapter 7 Notetaking Guide
Guided Practice Graph the function. 1. y x. y x. y x 1 1 y 1 y 1 y 1 x 1 x 1 x EXAMPE Writing and Graphing a Function The cost of gasoline is $1.50 per gallon. Write and graph a function that represents the cost y of x gallons of gasoline. WATCH UT! In Example, note that you cannot have less than 0 gallons of gasoline, so you cannot use any numbers less than 0 in the domain. The situation can be represented by the function, where y is the total cost of x gallons of gasoline. 1. Make an input-output table.. Plot the ordered pairs and connect them. Input x utput y 0 1 8 7 6 5 1 y 1 5 6 7 8 x esson 7.8 Graphing Functions 16
EXAMPE Identifying inear Functions Recall that a function pairs each input value with exactly one output value. Tell whether each graph represents a function of x. If it does, tell whether the function is linear. a. b. c. 1 y y 1 y 1 x 1 x 1 x Solution a. b. c. 16 Chapter 7 Notetaking Guide
E SSN 7.8 Name Practice B For use with pages 76 85 Date Identify the graph of the function on the coordinate plane. y 1. y 5x. y x. y 1 x 1 x Graph the function.. y x 5. y 8 x 6. y 1 x 7. y x 5 8. y x 6 9. y x 10. y 1 x 11. y 0.75x 1. y x 8 Write and graph a function that converts the units. 1. x feet to y inches 1. x pounds to y ounces 15. x months to y years Tell whether the graph represents a function of x. If it does, tell whether the function is linear or nonlinear. 16. y 17. y 18. 6 5 1 1 x 5 1 1 x y 1 5 6 x esson 7.8 19. When you are swimming, your body burns about 8 calories every minute. Write and graph a function that models the number of calories burned y after swimming for x minutes. 0. utdoor carpeting costs $1.5 for each square foot. Write and graph a function that models the cost y of x square feet of carpeting. 1. A phone company charges a $.5 dialing fee for calling a long-distance number and then charges $.10 for each minute of the call. This situation can be represented by the function y 0.1x 0.5, where y is the total cost of the call and x is the length of the call in minutes. Graph the function. Copyright McDougal ittell/houghton Mifflin Company All rights reserved. McDougal ittell Math, Course 79 Chapter 7 Resource Book
E SSN 7.8 Name Practice C For use with pages 76 85 Date Graph the function. 1. y x. y 9 x. y x. y x 5 5. y 6x 1 6. y 1 x 7. y 0.5x 1.5 8. y x 11 9. x y Write and graph a function that converts the units. 10. x inches to y feet 11. x quarts to y cups 1. x years to y months Tell whether the graph represents a function of x. If it does, tell whether the function is linear or nonlinear. 1. y 1. y 15. 1 1 1 y 1 x 1 x 1 5 6 x esson 7.8 Graph the functions in the same coordinate plane. Then tell where they intersect. 16. y x and y x 1 17. y x and y 9 x 18. y x and y 5x 8 19. When you are jogging, your body burns about 10 calories every minute. Write and graph a function that models the number of calories burned y after jogging for x minutes. 0. utdoor carpeting costs $1.75 for each square foot. Write and graph a function that models the cost y of x square feet of carpeting. 1. A phone company charges a $.50 dialing fee for calling a long-distance number and then charges $.1 for each minute of the call. This situation can be represented by the function y 0.1x 0.5, where y is the total cost of the call and x is the length of the call in minutes. Graph the function.. Graph the functions y x and y x in the same coordinate plane and tell where they intersect. Then solve the equation x x. What do you notice? 80 McDougal ittell Math, Course Chapter 7 Resource Book Copyright McDougal ittell/houghton Mifflin Company All rights reserved.