Download Algebra 2A 2016: Solving Compound and Absolute Value Inequalities

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Algebra 2A 2016: Solving Compound and Absolute Value Inequalities
Compound Inequalities A compound inequality consists of two inequalities joined by
the word and or the word or. To solve a compound inequality, you must solve each part
separately.
And
Compound
Inequalities
Example: x 4 and x 3
Or
Compound
Inequalities
Example: x 3 or x 1
5 4 3 2 1 0
1
2
New Vocabulary
The graph is the intersection of solution sets of
two inequalities.
3
4
compound inequality
intersection
5
union
5 4 3 2 1 0
1
2
The graph is the union of solution sets of
two inequalities.
3
4
5
Write an absolute value inequality for each of the following. Then graph the
solution set on a number line.
1. all numbers greater than or equal to 2
or less than or equal to 2
4 3 2 1 0
1
2
3
1
2
3
8 6 4 2 0
4
3. all numbers less than 1 or greater
than 1
4 3 2 1 0
2. all numbers less than 5 and greater
than 5
2
4
6
8
4. all numbers between 6 and 6
8 6 4 2 0
4
2
4
6
8
Write an absolute value inequality for each graph.
5.
6.
4 3 2 1 0
1
2
3
4
4 3 2 1 0
1
2
3
4
7.
4 3 2 1 0
1
2
3
4
4 3 2 1 0
1
2
3
4
8.
Solve each inequality. Graph the solution set on a number line.
9. 2c 1 5 or c 0
4 3 2 1 0
1
2
3
10. 11 4y 3 1
4
11.8 3x 2 23
0
1
2
3
4
5
4 3 2 1 0
1
2
3
4
12. w 4 10 or 2w 6
6
7
8
4 3 2 1 0
1
2
3
4
For all real numbers a and b, b 0, the following statements are true.
1. If ⏐a⏐ b, then b a b.
2. If ⏐a⏐ b, then a b or a b.
These statements are also true for and .
13. ⏐x 8⏐ 3
14. ⏐2z 2⏐ 3
15. ⏐2x 2⏐ 7 5
16. ⏐x⏐ x 1
17. ⏐3b 5⏐ 2
18. ⏐3n 2⏐ 2 1
19. RAINFALL In 90% of the last 30 years, the rainfall at Shell Beach has varied no more
than 6.5 inches from its mean value of 24 inches. Write and solve an absolute value
inequality to describe the rainfall in the other 10% of the last 30 years.
20. MANUFACTURING A company’s guidelines call for each can of soup produced not to vary
from its stated volume of 14.5 fluid ounces by more than 0.08 ounces. Write and solve an
absolute value inequality to describe acceptable can volumes.