SECTION 2.6 Set Operations and Compound Inequalities 109
Concept Check Two sets are specified by graphs. Graph the intersection of the two sets.
17. 18.
–3 0 2–3 0 20 50 52 52 500 636300For each compound inequality, give the solution set in both interval and graph form. See
Examples 2 – 4.
- and 20. and
- and 22. and
- and 24. and
- and 26. and
- and 28. and
- and 30. and
Concept Check Two sets are specified by graphs. Graph the union of the two sets.
33. 34.
3 x- 4 ... 8 - 4 x+ 1 Ú- 15 7 x+ 6 ... 48 - 4 xÚ- 24- 3 x 73 x+ 370 - 3 x 63 x+ 266
x- 3 ... 6 x+ 2 Ú 7 x+ 5 ... 11 x- 3 Ú- 1x... 3 xÚ 6 x...- 1 xÚ 3x... 2 x... 5 xÚ 3 xÚ 6x 62 x7- 3 x 65 x 70042042–5 0 6–5 0 681 81001 8 001 8For each compound inequality, give the solution set in both interval and graph form. See
Examples 6 – 8.
- or 36. or
- or 38. or
- or 40. or
- or 42. or
- or 44. or
- or 46. or
Concept Check Express each set in the simplest interval form. (Hint: Graph each set and
look for the intersection or union.)
For each compound inequality, decide whether intersectionor unionshould be used. Then
give the solution set in both interval and graph form. See Examples 2 – 4 and 6 – 8.
- and 56. and
57.x 64 or x6- 2 58.x 65 or x6- 3
x6- 1 x7- 5 x7- 1 x 673 3, 6 4 ́ 1 4, 9 2 3 - 1, 2 4 ́ 1 0, 5 2
1 - q, 3 2 ́ 1 - q, - 22 3 - 9, 1 4 ́ 1 - q, - 321 - q, - 64 ̈ 3 - 9, q 2 1 5, 11 4 ̈ 3 6, q 21 - q, - 14 ̈ 3 - 4, q 2 3 - 1, q 2 ̈ 1 - q, 9 44 x+ 1 Ú- 7 - 2 x+ 3 Ú 5 3 x+ 2 ...- 7 - 2 x+ 1 ... 9x+ 173 - 4 x+ 175 3 x 6 x+ 12 x+ 1710x+ 277 1 - x 76 x+ 173 x+ 462xÚ- 2 x... 4 xÚ 5 x... 7xÚ- 2 xÚ 5 x...- 2 x... 6x... 1 x... 8 xÚ 1 xÚ 8