Worksheet 2-4 P. 2

IMrtlVIt

2-4 Absolute Value in Open Sentences (continued) Example 3

Solve |4* — 51 > 9 and graph its solution set.

Solution

Write 14* — 5| > 9 as the equivalent disjunction:

4* - 5 < -9 4* < -4 * < -1

4*-5>9 4* > 14

or or or

H r-e-H - 2 - 1 0 1 2 3 4

.'. the solution set is *: * < — 1 or * > — <-

2J

Check: Test a point in each of the shaded regions and a point between them. Try* = -2: |4(-2) - 5| = |-8 - 5| = | - 13| = 13 > 9 True V Try* = 4: |4 • 4 - 5| = |16 - 5| = |ll| = 11 > 9 True V Try* = 0: |4 • 0 - 5| = |0 - 5| = | -5| = 5 > 9 False V

Example 4

Solve 15 — 2* - 1 < 2 and graph its solution set.

Solution

Rewrite the inequality so that the absolute value is alone on one side. |5 - 2*| - 1 < 2 |5 - 2*| < 3 Write 5 - 2 * | < 3 as the equivalent conjunction: -3 < 5 - 2* < 3 -8 < -2* < -2 4 > * > 1 .'. the solution set is {*: 1 < * < 4). 1 }

-

1

0

1

2

3

4

5

Check: Test a point in the shaded region and a point on either side of it. Try* - 2: |5 - 2 • 2| = |5 - 4| = |l| = 1 < 3 True V Try* = 0: 5 - 2 • 0| = 5 - 0| = |5| = 5 < 3 False V Try* = 5: 5 - 2 • 5| = |5 - 10| = | -5 = 5 < 3 False V Solve and graph the solution set.

13. 17. 21. 25. 29. 33.

26

\r > 2 \g - 4| > 2 6 < \2m - 3| |2n + 3| > -2 |4 - 3*| > 5 2 2

** > 1 3*

14. \k\ < 5 18. |z - 1| < 2 22. \3h + 1 > 5 26. |2 - q\ > 5 30. |6 - 4w\ > 2

34.

m +1 2

T^ "

15. |-3m| > 0 19. 0 > |* - 7|

16. |/ + 2| > 3

23. \5p - 4| < 1

20. 12? + 1| < 5 24. |3* - 2| < 4

27. |3 - a\ i= 2 31. |6 - 7c| < -1

28. |1 - 26| < 3 32. |3 - 0.4y| < 7

«Jw •

«^\*»

I I

T

-ii

^v _/

|f

i

A

^

~^»

l.

Study Guide, ALGEBRA AND TRIGONOMETRY, Structure and Method, Book 2 Copyright © by Houghton Mifflin Company. All rights reserved.