36.Concept Check The graph of the solution set of is given here.Without actually doing the algebraic work, graph the solution set of the following, refer-
ring to the graph shown.
(a) (b)Solve each inequality, and graph the solution set. See Example 3.(Hint: Compare your an-
swers with those in Exercises 23 – 34.)
In Exercises 49 – 66, decide which method of solution applies, and find the solution set.
In Exercises 49 – 60, graph the solution set. See Examples 1–3.
Solve each equation or inequality. See Examples 4 and 5.
77.|0.1x-2.5|+0.3Ú0.8 78.|0.5x-3.5|+0.2Ú0.6`
2
3
x+1
6
` +
1
2
=
5
2
`
1
2
x+1
3
` +
1
4
=
3
4
|x+ 5 |- 6 ...- 1 |x- 2 |- 3 ... 4|x+ 5 |- 2 = 12 | 2 x+ 1 |+ 378 | 6 x- 1 |- 276|x|- 1 = 4 |x|+ 3 = 10 |x+ 4 |+ 1 = 2|x- 4 |= 1 | 2 - 0.2x|= 2 | 5 - 0.5x|= 4|x+ 2 |= 3 |x+ 3 |= 10 |x- 6 |= 3|- 2 x- 6 |... 5 | 2 x- 1 |Ú 7 |- 4 +x|... 9| 3 x- 1 |... 11 | 2 x- 6 |... 6 |- 6 x- 6 |... 1| 2 x- 1 | 67 | 7 + 2 x|= 5 | 9 - 3 x|= 3|- 4 +x| 79 |- 3 +x| 78 |x+ 5 | 720| 5 - x|... 3 |- 5 x+ 3 | 612 |- 2 x- 4 | 65|x+ 2 |... 10 | 4 x+ 1 | 621 | 3 - x|... 5|x| 66 |r+ 5 | 620 | 3 r- 1 | 68|x|... 3 |x|... 5 |x| 64| 3 x- 4 |= 5 | 3 x- 4 | 75| 3 x- 4 | 65SECTION 2.7 Absolute Value Equations and Inequalities 119
Solve each equation. See Example 6.
82. 83. 84.
85. 86.
Solve each equation or inequality. See Examples 7 and 8.
102.|x- 4 |+ 5 Ú 4 103.| 10 x+ 7 |+ 361 104.| 4 x+ 1 |- 2 6- 5
| 5 x- 2 |= 0 | 7 x+ 4 |= 0 |x- 2 |+ 3 Ú 2|x+ 9 |7- 3 | 7 x+ 3 |... 0 | 4 x- 1 |... 0| 2 x- 1 |=- 6 | 8 x+ 4 |=- 4 |x+ 5 |7- 9| 13 x+ 1 |=- 3 | 4 x+ 1 |= 0 | 6 x- 2 |= 0|x|Ú- 10 |x|Ú- 15 | 12 t- 3 |=- 8| 2 x- 6 |=| 2 x+ 11 | | 3 x- 1 |=| 3 x+ 9 |` | 6 x|=| 9 x+ 1 | | 13 x|=| 2 x+ 1 |2
3
x- 2 ` = `1
3
x+ 3 `` x-1
2
=
1
2
| 3 x+ 1 |=| 2 x+ 4 | | 7 x+ 12 |=|x- 8 | x- 2 `30
1- 3