Practice and Problem-Solving Exercises

A Practice

See Problem 1.

Write a compound inequality that represents each phrase. Graph the solutions.

9. all real numbers that are between − 5 negative 5  and 7
10. The circumference of a women's basketball must be between 28.5 in. and 29 in., inclusive.

See Problems 2 and 3.

Solve each compound inequality. Graph your solutions.

11. − 4 < k + 3 < 8 negative 4 less than k plus 3 less than 8
12. 5 ≤ y + 2 ≤ 11 5 less than or equal to y plus 2 less than or equal to 11
13. 3 < 4 p − 5 ≤ 15 3 less than 4 p minus 5 less than or equal to 15
14. 15 ≤ 20 + 11 + k 3 ≤ 19 15 less than or equal to . fraction 20 plus 11 plus k , over 3 end fraction . less than or equal to 19
15. 1 4 < 2 x − 7 2 < 5 1 fourth , less than . fraction 2 x minus 7 , over 2 end fraction . less than 5
16. − 3 ≤ 6 − q 9 ≤ 3 negative 3 less than or equal to . fraction 6 minus q , over 9 end fraction . less than or equal to 3

See Problem 4.

Solve each compound inequality. Graph your solutions.

17. 6 b − 1 < − 7  or  2 b + 1 > 5 6 b minus 1 less than negative 7 , or , 2 b plus 1 greater than 5
18. 5 + m > 4  or  7 m < − 35 5 plus m greater than 4 , or , 7 m less than negative 35
19. 4 d + 5 ≥ 13  or  7 d − 2 < 12 4 d plus 5 greater than or equal to 13 , or , 7 d minus 2 less than 12
20. 7 − c < 1  or  4 c ≤ 12 7 minus c less than 1 , or , 4 c less than or equal to 12
21. 5 y + 7 ≤ − 3  or  3 y − 2 ≥ 13 5 y plus 7 less than or equal to negative 3 , or , 3 y minus 2 greater than or equal to 13
22. 5 z − 3 > 7  or  4 z − 6 < − 10 5 z minus 3 greater than 7 , or , 4 z minus 6 less than negative 10

See Problem 5.

Write each interval as an inequality. Then graph the solutions.

23. ( − ∞ , 2 ] open negative infinity comma 2 right bracket
24. [ − 4 , 5 ] left bracket negative 4 comma 5 right bracket
25. ( − ∞ , − 1 ]  or  ( 3 , ∞ ) open negative infinity comma negative 1 right bracket , or , open 3 comma infinity close
26. [ 6 , ∞ ) left bracket 6 comma infinity close

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