Summary Exercises on Solving Linear and Absolute Value Equations and Inequalities 121
Solve each equation or inequality. Give the solution set in set notation for equations and in
interval notation for inequalities.19. 20.
21. 22.
23. 24.
25. 26.
27. 28.
29. 30.
31. 32.
33. 34.
35. 36.
37. 38.
39. 40.
41. 42.
43. 44.
45. 46.
- 2 x+ 175 or 3 x+ 461 48. 1 - 2 xÚ 5 and 7 + 3 xÚ- 2
|x- 5 |=|x+ 9 | |x+ 2 |6- 38 x- 11 - x 2 = 311 + 3 x 2 - 4 8 x- 1 x+ 32 =- 12 x+ 12 - 12|x- 1 |Ú- 6 | 2 x- 5 |=|x+ 4 |- 6 ... | 5 - x| 64
3
2
- x... 6
x
6-
3 x
5- 1 x+ 42 + 2 = 3 x+ 8 =x- 86
1
2
...
2
3
x...5
4
| 1 - 3 x|Ú 4| 7 x- 1 |=| 5 x+ 3 | |x+ 2 |=|x+ 4 |- 2 ... 3 x- 1 ... 8 - 1 ... 6 - x... 5
| 5 x+ 1 |... 0 5 x- 13 +x 2 Ú 213 x+ 12x
4-
2 x
3| 2 x- 3 | 711 =- 10x+ 9 + 7 x= 413 + 2 x 2 - 3 6 - 312 - x 26211 +x 2 + 3|x- 1 | 673
5
x-1
10
= 2
7 x- 3 + 2 x= 9 x- 8 x1
4
x6- 6-
5
8
xÚ- 202
3
x+ 8 =1
4
x|x| 6 5.5 4 x- 1 = 12 +x9 x- 5 Ú 9 x+ 3 13 x- 5713 x- 89 x- 31 x+ 12 = 8 x- 7 |x|Ú 86 x- 5 ... 3 x+ 10 | 5 x- 8 |+ 9 Ú 72 x- 1 =- 7 | 3 x- 7 |- 4 = 08 x+ 2 Ú 5 x 41 x- 112 + 3 x= 20 x- 31|x+ 3 |=- 4 2 x+ 1 ...x6 x- 9 = 12 + 3 x 3 x+ 7 = 9 + 8 x4 x+ 1 = 49 |x- 1 |= 6SUMMARY EXERCISESon Solving Linear and Absolute Value Equations and Inequalities