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Chapter Summary and Review continued
6.5
Examples on
pp. 348–350
SOLVING COMPOUND INEQUALITIES INVOLVING “OR”
EXAMPLE
Solve the compound inequality x 3 ≤ 7 or 4x > 20. Then graph the solution.
Solve each of the parts separately.
x3≤7
or
4x > 20
Write original inequality.
x33≤73
or
4x 20
> 4
4
Isolate x.
or
x>5
Simplify.
x≤4
ANSWER 䊳
The solution is all real numbers less than or equal to 4 or greater than 5.
The graph of the solution is shown below.
0
1
2
3
4
5
6
7
Solve the inequality. Then graph the solution.
6.6
28. x > 4 or 3x ≤ 9
29. 2x ≤ 10 or x 3 > 1
30. x 7 ≥ 0 or 3 x < 2
31. 6x 2 ≤ 4 or 3x > 21
32. 3x 2 ≤ 7 or 2x 1 ≥ 9
1
1
33. x < or 3x 6 > 24
4
2
Examples on
pp. 355–357
SOLVING ABSOLUTE-VALUE EQUATIONS
EXAMPLE
Solve ⏐x 4⏐ 6.
Because ⏐x 4⏐ 6, the expression x 4 is equal to 6 or 6.
X 4 IS POSITIVE
or
X 4 IS NEGATIVE
x46
x 4 6
x4464
x 4 4 6 4
x 10
ANSWER 䊳
CHECK
x 2
or
The equation has two solutions: 10 and 2.
✓ ⏐10 4⏐ ⏐6⏐ 6
⏐2 4⏐ ⏐6⏐ 6
Solve the equation and check your solutions. If the equation has no
solution, write no solution.
34. ⏐x⏐ 13
35. ⏐x⏐ 7
36. ⏐x 1⏐ 6
37. ⏐3x⏐ 27
38. ⏐2x 3⏐ 1
39. ⏐6x 1⏐ 5 2
40. Write an absolute-value equation that has 9 and 21 as its solutions.
Chapter Summary and Review
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