Practice and Problem-Solving Exercises

A Practice

See Problem 1.

Solve each inequality. Check your solutions.

9. 5 f + 7 ≤ 22 5 f plus 7 less than or equal to 22
10. 6 n − 3 > − 18 6 n minus 3 greater than negative 18
11. − 5 y − 2 < 8 negative 5 y minus 2 less than 8
12. 6 − 3 p ≥ − 9 6 minus 3 p greater than or equal to negative 9
13. 9 ≤ − 12 + 6 r 9 less than or equal to negative 12 plus 6 r
14. 6 ≤ 12 + 4 j 6 less than or equal to 12 plus 4 j

See Problem 2.

Write and solve an inequality.

15. Family Trip On a trip from Buffalo, New York, to St. Augustine, Florida, a family wants to travel at least 250 mi in the first 5 h of driving. What should their average speed be in order to meet this goal?
16. Geometry An isosceles triangle has at least two congruent sides. The perimeter of a certain isosceles triangle is at most 12 in. The length of each of the two congruent sides is 5 in. What are the possible lengths of the remaining side?

See Problems 3 and 4.

Solve each inequality.

17. 3 ( k − 5 ) + 9 k ≥ − 3 3 open k minus 5 close plus 9 k greater than or equal to negative 3
18. − ( 7 c − 18 ) − 2 c > 0 negative open 7 c minus 18 close minus 2 c greater than 0
19. − 3 ( j + 3 ) + 9 j < − 15 negative 3 open j plus 3 close plus 9 j less than negative 15
20. − 4 ≤ 4 ( 6 y − 12 ) − 2 y negative 4 less than or equal to 4 open 6 y minus 12 close minus 2 y
21. 30 > − ( 5 z + 15 ) + 10 z 30 greater than negative open 5 z plus 15 close plus 10 z
22. − 4 ( d + 5 ) − 3 d > 8 negative 4 open d plus 5 close minus 3 d greater than 8
23. 4 x + 3 < 3 x + 6 4 x plus 3 less than 3 x plus 6
24. 4 v + 8 ≥ 6 v + 10 4 v plus 8 greater than or equal to 6 v plus 10
25. 5 f + 8 ≥ 2 + 6 f 5 f plus 8 greater than or equal to 2 plus 6 f
26. 6 − 3 p ≤ 4 − p 6 minus 3 p less than or equal to 4 minus p
27. 3 m − 4 ≤ 6 m + 11 3 m minus 4 less than or equal to 6 m plus 11
28. 4 t + 17 > 7 + 5 t 4 t plus 17 greater than 7 plus 5 t

See Problem 5.

Solve each inequality, if possible. If the inequality has no solution, write no solution. If the solutions are all real numbers, write all real numbers .

29. − 3 ( w − 3 ) ≥ 9 − 3 w negative 3 open w minus 3 close greater than or equal to 9 minus 3 w
30. − 5 r + 6 ≤ − 5 ( r + 2 ) negative 5 r plus 6 less than or equal to negative 5 open r plus 2 close
31. − 2 ( 6 + s ) ≥ − 15 − 2 s negative 2 open 6 plus s close greater than or equal to negative 15 minus 2 s
32. 9 + 2 x < 7 + 2 ( x − 3 ) 9 plus 2 x less than 7 plus 2 open x minus 3 close
33. 2 ( n − 8 ) < 16 + 2 n 2 open n minus 8 close less than 16 plus 2 n
34. 6 w − 4 ≤ 2 ( 3 w + 6 ) 6 w minus 4 less than or equal to 2 open 3 w plus 6 close

B Apply

Solve each inequality, if possible. If the inequality has no solution, write no solution. If the solutions are all real numbers, write all real numbers .

35. − 3 ( x − 3 ) ≥ 5 − 4 x negative 3 open x minus 3 close greater than or equal to 5 minus 4 x
36. 3 s + 6 ≤ − 5 ( s + 2 ) 3 s plus 6 less than or equal to negative 5 open s plus 2 close
37. 3 ( 2 + t ) ≥ 15 − 2 t 3 open 2 plus t close greater than or equal to 15 minus 2 t
38. 4 3 s − 3 < s + 2 3 − 1 3 s 4 thirds , s minus 3 less than s plus , 2 thirds , minus , 1 third , s
39. 4 − 2 n ≤ 5 − n + 1 4 minus 2 n less than or equal to 5 minus n plus 1
40. − 2 ( 0.5 − 4 t ) ≥ − 3 ( 4 − 3.5 t ) negative 2 open 0.5 minus 4 t close greater than or equal to negative 3 open 4 minus 3.5 t close
41. 4 ( a − 2 ) − 6 a ≤ − 9 4 open eh minus 2 close minus 6 eh less than or equal to negative 9
42. 4 ( 3 n − 1 ) ≥ 2 ( n + 3 ) 4 open 3 n minus 1 close greater than or equal to 2 open n plus 3 close
43. 17 − ( 4 k − 2 ) ≥ 2 ( k + 3 ) 17 minus open 4 k minus 2 close greater than or equal to 2 open k plus 3 close
44. Think About a Plan Your cell phone plan costs $39.99 per month plus $.15 for each text message you send or receive. You have at most $45 to spend on your cell phone bill. What is the maximum number of text messages that you can send or receive next month?
    • What information do you know? What information do you need?
    • What inequality can you use to find the maximum number of text messages that you can send or receive?
    • What are the solutions of the inequality? Are they reasonable?

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