Worksheet 2-2 P. 2

NAME

2-2

DATE

Solving Combined Inequalities (continued)

Example 4

Solve — 1 < 3x — 4 < 8 and graph its solution set.

Solution 1

Rewrite the inequality using and. Then solve each inequality. -1 < 3x -4 3 < 3x 1 < x

3x - 4 < 8 3jc < 12 x < 4

and and and

-

Solution 2

0

1

2

3

4

5

Solve both inequalities simultaneously -1 < 3x - 4 < 8 -l+4<3jc-4 + 4 < 8 + 4 3 < 3* < 12 3 < 3

3x 3

< 12 3

1 <

x

< 4

Add 4 to each expression. Divide each expression by 3.

.'. the solution set is {x: 1 < x < 4}

Example 5

1

(See graph above.)

Solve the disjunction 5 + 3x < 2 or 2x — 2 > 4 — x and graph its solution set.

Solution

5 + 3x < 2

or

5 + 3 x - 5 < 2 - 5 3x < -3 x < - 1

or or or

2x - 2 > 4 - x 2x - 2 + 2 + x > 4 - x + 2 + x 3x > 6 x > 2 -3 -2 - 1 0

1

2

3

Solve each conjunction or disjunction and graph each solution set that is not empty. 9. 0 < x - 1 < 4

10.

1 > jfc + 3 >

-2

11. y - \ < 3 and v + 3 > 3

12. x + 3 < 2 or jc - 6 >

13. w + 2< 3 and 2 - w < 5

14. -2 < 1 - t < 4

15. 4 - 3jc < -2 or.r < 0

16. - 1 < 2m + 1 < 3

17. 2* + 3 > 9 and 5x - 1 < 9

18. 3x - 1 > 2 or IT + 6 < 2

19. 2n + 5 < 3 or2(« - 1 ) > 0

20. 3z + 1 > 7 and 2fe - 1) <

21. 5 j t - 2 > 8 o r 4 - j c > 5

22. 3 < 4 - 2r < 6

23. 3p - 5 < 1 or 4 - 2p < 6

24. 3 > - -!- 3 > 2 4

22

-2

-4

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