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Algebra Chapter 2 Review Name________________Date____ Period______
Solve the inequality.
1. 7 w 1 w 5 2. 3 g 5 3 g 3. 2 h 2 2 1 h
4. You are saving $12 per week to purchase a new kayak. Prices start at $300 and go up. Your
parents give you $144 to help you purchase your kayak. Write and solve an inequality to find the
number of weeks you need to save to purchase the kayak.
Write and graph a compound inequality that represents the numbers that are NOT solutions of the inequality represented by the graph shown.
5.
Solve the inequality. Graph the solution.
7. 1 9 n 17 8. 50 7 k 6 8 9. g 5 12 or^ g 9^ 0
10. 8 t 8 64 and 7 8 t 79 11. 2 x 10 or 3
x
12. A bike shop rents bikes with heights ranging from 18 inches to 26 inches. The shop says the height
of the bike should be about 0.6 times a cyclist's leg length. Write and solve a compound
inequality that represents the leg lengths of the cyclists the shop does not provide bikes for.
In Exercises 1 3 – 16 , solve the inequality. Graph the solution, if possible.
13. 24 5 t 4 16 14. 3 p 2 4 or 7 p 28
15. n 5 9 and n 3 8 16. a 6 3 or 3 a 2 8
In Exercises 1 7 - 22 solve the inequality. Graph the solution, if possible.
17. y 4 18. h 7 5 19. 4 x 12 7
20. 2 x 8 10 21. 4 w 7 8 17 22. 10 4 x 14
23. The ideal diameter of a piston for a car is 88 millimeters, and the actual diameter can vary from the ideal diameter by
at most 0.007 millimeter. Write and solve an absolute value inequality that represents the actual diameter.
24. In a poll of 100 people, you have an approval rating as class president of 78% with a 3% margin of
error. Write and solve an absolute value inequality that represents your approval rating.
25. Describe and correct the error in solving the absolute value inequality.
2 3 or 2 3 5 or 1
x x x x x
Write the sentence as an absolute value inequality. Then solve the inequality.
26. A number is less than 4 units from 0.
27. A number is more than 11 units from 8.
28. Half a number is at least 2 units from 20.
29. Solve the literal equation for x.
a. y 5 x 2 x b. r x 9 x
c. b 3 x 9 xy d. w 2 hx 11 x
e. p 4 x qx 5 f. m 9 3 x dx
30. Solve the equation. Check your solutions.
a. 9 w 4 2 w 10 b. 2 n 7 4 n 8
15. n 5 9 and n 3 8 16. a 6 3 or 3 a 2 8
n 5 all real numbers
In Exercises 1 02 – 107 , solve the inequality. Graph the solution, if possible.
17. y 4 18. h 7 5 19. 4 x 12 7
4 y 4 h 2 or h 12 all real numbers
20.^2 x^ ^8 ^10 21.^4 w^ ^7 ^8 ^17 22.^10 ^4 x ^14
. no solution w 4 or w ^12 6 x 1
23. The ideal diameter of a piston for a car is 88 millimeters, and the actual diameter can vary from
the ideal diameter by at most 0.007 millimeter. Write and solve an absolute value inequality that
represents the actual diameter.
x 88 0.007; 87.993 x 88.
24. In a poll of 100 people, you have an approval rating as class president of 78% with a 3% margin
of error. Write and solve an absolute value inequality that represents your approval rating.
x 78 3; 75 x 81
25. Describe and correct the error in solving the absolute value inequality.
2 3 or 2 3 5 or 1
x x x x x
x 2 3; There is no solution.
Write the sentence as an absolute value inequality. Then solve the inequality.
26. A number is less than 4 units from 0.
x 4; 4 x 4
27. A number is more than 11 units from 8.
x 8 11; x 3 or x 19
28. Half a number is at least 2 units from 20.
(^12) x 20 2; x 44 or x 36
30. Solve the literal equation for x****.
a. y 5 x 2 x x 3^ y b. r x 9 x x 10^ r
c. b 3 x 9 xy x 3 ^ b 9 y d. w 2 hx 11 x 𝑥 = 2ℎ𝑤− 11
e. p 4 x qx 5 x 4^ p ^ q^5 f. m 9 3 x dx x 3^ m ^ d^9
31. Solve the equations. Check your solutions.
a.^9 w^ ^4 ^2 w ^10 b.^2 n^ ^7 ^4 n ^8
w 2 and w 116 𝑛^ =^3 and^ 𝑛^ =^ −^11 3
