Algebra 2: Linear Equations and Inequalities in One Variable
Topic B7: Absolute Value Inequalities | VERSION B Name: ________________________________________ 6.
Solve the following inequalities then graph the solution sets. 1.
𝑥 − 8 < 3 𝑥 ≤ 2 −10
−10
0
10
0
10
0
25
0
10
0
10
𝑥 > 1 −10
0
10
8.
𝑥 − 6 ≥ 2 𝑥 − 4 < −2 −25
−10
0
10
9.
4.
𝑥 + 3 ≤ −8 −10
3.
10
7.
2.
0
2𝑥 − 1 ≥ 7 𝑥 + 3 ≥ 5 −10
−10
0
10
10. 2𝑥 + 3 + 5 < 6 5.
𝑥 ≥ −12 −10
−10
0
10
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Name: ________________________________________ Topic B7: Absolute Value Inequalities | VERSION B Solve the inequalities. Answer in interval notation. 11. 𝑥 + 5 ≤ 4 Solve the following inequalities and then graph the solution sets. Keep in mind that if you multiply or divide both sides by a negative number, you must reverse the sense of the inequality. 18. 2 − 𝑥 > 4 12. 𝑥 − 5 > 8 −10
13. −6𝑥 − 2 ≤ 8 19.
0
10
0
25
1
𝑥 + 4 > 2 2
−25
14. −6𝑥 + 1 ≤ 5 When white light from the sun passes through a prism, it is broken down into bands of light that form colors. The wavelength, v, (in nanometers) of some common colors are: 1
3
15. 2𝑥 + 4 > 16.
4𝑥−3
1
> 4
7
17. 4𝑥 −
Blue: 424 < v < 491 Green: 491 < v < 575 Yellow: 575 < v < 585 Orange: 585 < v < 647 Red: 647 < v < 700 20. When a fireworks display made of calcium chloride is burned, it lets out light with wavelengths, v, that satisfy the relationship 𝑣 − 620 < 25. a.
Write this inequality without absolute values, find the range of possible values for v. b.
Determine the color that calcium chloride fireworks display. 1
7
≤ 3
10
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Topic B7: Absolute Value Inequalities | VERSION B Name: ________________________________________ 6.
Solve the following inequalities then graph the solution sets. 1.
𝑥 − 8 < 3 (5, 11) 𝑥 ≤ 2 [−2, 2] −10
−10
0
10
0
10
10
10
10
𝑥 > 1 (−∞, −1) ∪ (1, ∞) −10
0
10
8.
𝑥 − 6 ≥ 2 −∞, 4 ∪ [8, ∞) 𝑥 − 4 < −2 (−2, 2) −10
−10
0
10
0
9.
4.
𝑥 + 3 ≤ −8 DNE −10
3.
10
7.
2.
0
2𝑥 − 1 ≥ 7 −∞, −3 ∪ [4, ∞) 𝑥 + 3 ≥ 5 −∞, −2 ∪ [2, ∞) −10
−10
0
10
0
10. 2𝑥 + 3 + 5 < 6 (−2, −1) 5.
𝑥 ≥ −12 (−∞, ∞) −10
−10
0
10
0
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Name: ________________________________________ Topic B7: Absolute Value Inequalities | VERSION B Solve the inequalities. Answer in interval notation. 11. 𝑥 + 5 ≤ 4 [−9, −1] Solve the following inequalities and then graph the solution sets. Keep in mind that if you multiply or divide both sides by a negative number, you must reverse the sense of the inequality. 18. 2 − 𝑥 > 4 (−∞, −2) ∪ (6, ∞) 12. 𝑥 − 5 > 8 −∞, −3 ∪ 13, ∞ −10
5
13. −6𝑥 − 2 ≤ 8 − , 1 3
10
25
1
𝑥 + 4 > 2 (−∞, −12) ∪ (−4, ∞) 2
19.
−25
2
3
0
0
14. −6𝑥 + 1 ≤ 5 − , 1 1
3
15. 2𝑥 + 4 > −∞, −
When white light from the sun passes through a prism, it is broken down into bands of light that form colors. The wavelength, v, (in nanometers) of some common colors are: 4𝑥−3
1
17
25
16.
> −∞,
∪ , ∞ 4
7
28
8
17. 4𝑥 −
Blue: 424 < v < 491 Green: 491 < v < 575 Yellow: 575 < v < 585 Orange: 585 < v < 647 Red: 647 < v < 700 13
11
∪ − , ∞ 6
6
20. When a fireworks display made of calcium chloride is burned, it lets out light with wavelengths, v, that satisfy the relationship 𝑣 − 620 < 25. a.
Write this inequality without absolute values, find the range of possible values for v. −25 < 𝑣 − 620 < 25 range: (595, 645) b.
Determine the color that calcium chloride fireworks display. Orange 1
7
11
31
≤ −
,
3
10
120 120
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