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What is the first step you would use to solve the inequality?

1. 8x 1 6 < 1 2. –10 > 3a 2 5

3. 2( y 2 1) ≥ 9 4. 2( p 2 5) < 13

5. 4n 2 3 > 2n 6. 6b 1 1 ≥ 9 2 4b

Match the verbal sentence with the inequality.

7. Three more than 2 times a number x is greater than 27. A. 2 1 3x > 27

8. Twice the sum of 3 and a number x is greater than 27. B. 3 1 2x > 27

9. Three times the sum of 2 and a number x is greater than 27. C. 2(3 1 x) > 27

10. Two more than 3 times a number x is greater than 27. D. 3(2 1 x) > 27

Solve the inequality. Graph your solution.

11. 2x 1 4 ≥ 6 12. 3p 2 1 < 5

13. 5n 1 8 ≥ 27 14. 4a 2 9 ≤ 225

15. 22y 1 3 ≥ 3 16. 21 2 4c < 3

17. 5(m 1 1) ≤ 20 18. 3( p 2 2) > 6

19. 7(x 2 4) ≤ 0 20. 4(w 1 6) ≥ 60

Practice AFor use with the lesson “Solve Multi-Step Inequalities”

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Solve the inequality, if possible.

21. 6x 1 2 ≤ 5x 1 2 22. 4y 1 1 > y 2 8 1 3y

23. 2x 2 8 1 3x ≥ 5x 2 4 24. 3(b 2 1) < 3b 1 3

25. 9a 2 6a 1 1 ≤ 1 1 3a 26. 8y 1 10 > 2(4y 1 7) 2 3

Translate the verbal phrase into an inequality. Then solve the inequalilty and graph your solution.

27. The sum of 4x and 7 is less than or equal to 39.

28. Three times the difference of x and 2 is greater than 221.

29. The sum of 5x and 8x is less than the sum of 4x and 27.

30. Greeting Cards Your school club is making greeting cards to raise money for a trip. You spend $60 on supplies and plan to sell the cards for $2 each.

a. Write an inequality that gives the possible numbers c of cards you need to sell in order for the profit to be positive.

b. What are the possible numbers of cards you need to sell in order for the profit to be positive?

31. Gasoline A grocery store chain that owns gasoline stations is offering its customers a deal. For every $50 customers spend on groceries, the service station charges $.10 less per gallon of gasoline.

a. If gasoline costs $2.15 per gallon, how much will it cost per gallon if you spend $50 at the grocery store?

b. Write an inequality that gives the possible numbers g of gallons of gasoline you can buy if you spend exactly $50 on groceries and want to spend at most $60 on groceries and gasoline.

c. What are the possible numbers of whole gallons of gasoline you can buy?

Practice A continuedFor use with the lesson “Solve Multi-Step Inequalities”

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Lesson Solve Multi-Step Inequalities

Teaching Guide

1. A 5 250, B 5 0.25x 1 150

2. The 0.25x 1 150 > 250 represents how many miles you must drive in order for the cost of renting a car from Company B to be greater than the cost of renting a car from Company A. 3. You can solve the inequality in much the same way you can solve an equation. First subtract 150 from each side, then divide each side by 0.25 to obtain x > 400.

Practice Level A

1. Subtract 6 from each side.

2. Add 5 to each side. 3. Use the distributive property. 4. Use the distributive property.

5. Add 3 to each side. 6. Sample answer: Add 4b to each side. 7. B 8. C 9. D 10. A

11. x ≥ 1; 021222324 1 2 3 4

12. p < 2; 021222324 1 2 3 4

13. n ≥ 23; 021222324 1 2 3 4

14. a ≤ 24; 022242628 2 4 6 8

15. y ≤ 0; 021222324 1 2 3 4

16. c > 21; 021222324 1 2 3 4

17. m ≤ 3; 021222324 1 2 3 4

18. p > 4; 022242628 2 4 6 8

19. x ≤ 4; 022242628 2 4 6 8

20. w ≥ 9; 0232629 3 6 9 12 15

21. x ≤ 0 22. all real numbers 23. no solution

24. all real numbers 25. all real numbers

26. no solution

27. 4x 1 7 ≤ 39; x ≤ 8

9 10 11 12 135 6 7 8

28. 3(x 2 2) > 221; x > 25

25262728 021222324

29. 5x 1 8x < 4x 1 27; x < 3

0 6543212122

30. a. 2c 2 60 > 0 b. more than 30 cards

31. a. $2.05 per gallon b. 50 1 2.05g ≤ 60 c. 4 gallons or less

Practice Level B

1. x ≥ 2; 021222324 1 2 3 4

2. p < 22; 021222324 1 2 3 4

3. n ≤ 29; 0232629212215 3 6 9

4. a ≤ 15; 02326 3 6 9 12 15 18

5. y > 0; 021222324 1 2 3 4

6. c > 12; 02326 3 6 9 12 15 18

7. m < 3; 021222324 1 2 3 4

8. d < 7 }

3 ;

73

21 0 3 421

9. z ≤ 7 }

8 ;

2122 0 21

78

10. w < 3; 021222324 1 2 3 4

11. no solution 12. all real numbers 13. c < 0

14. all real numbers 15. no solution

16. no solution 17. all real numbers 18. all real numbers 19. no solution 20. no solution

21. no solution 22. all real numbers 23. all real numbers 24. no solution

25. 6 1 5x ≥ 31; x ≥ 5;

021 1 2 3 4 5 6 7

26. 2(4 1 x) < 216; x < 212;

02428212216 4 8 12 16

27. 10x 2 3x ≤ 4x 1 21; x ≤ 7;

022242628 2 4 6 8

7

28. 2x 1 4x ≥ 2x 1 36; x ≥ 9;

0232629 3 6 9 12 15

29. 2x 2 15 ≤ 4x 1 17; x ≥ 216;

02428212216220 4 8 12

30. a. 80w 2 420 > 0 b. 6 wall hangings or more

31. a. 225 1 120p ≥ 400 b. 1.5 pins or more

32. At most 4 additional fish; First find the number of gallons needed by the 6 fish by finding the product of 6 and 2, which is 12. Then subtract this amount from 20 to get 8, the number of gallons left for new fish. Then solve the inequality 2f ≤ 8, where f is the number of new fish.

Algebra 1Chapter Resource Book A57

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