1. 1.7a - Absolute Value Inequalities
PAGE 45 3) 5) 7) 9)
11)
–3 < x < 1; x > –3 AND x < 1
13)
x < –2 OR x > 4
15) C
23)
x < –2; {x|x < –2}
(-∞, -2]
25)
x < 4; {x|x < 4}
(-∞, 4)
27)
x < 6; {x|x < 6}
(-∞, 6]
29)
x < –8; {x|x < 4}
31)
x < 1/2; {x|x < 1/2}
(-∞, ½) 4 4
33)
x < –7; {x|x < –7}
(-∞, –7)
35)
The inequality should not be reversed when subtracting
37)
–6 < x < 3; {x|–6 < x < 3}; (-6, 3)
39)
1 < x < 7; {x|1 < x < 7}
[1, 7) –7 –5 6 6
–3.5 –6 –8 3 1 7 –2
1/2
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1.7a - Absolute Value Inequalities

2. 1.7a - Absolute Value Inequalities
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1.7a - Absolute Value Inequalities

3. 1.7a - Absolute Value Inequalities
PAGE 45
41)
–3/2 < x < –1/2; {x|–3/2 < x < –1/2}; (-3/2, –1/2)
43)
x < –4 OR x > 2; {x|x < –4 OR x > 2}; (-3/2, –1/2)
45)
x < –1/2 OR x > 1; {x|x < –1/2 OR x > 1}; [-1/2, 1]
49)
No Solution
50)
All Real Numbers
51)
53)
45x + 35 < 250; x < 4 7/9 days
56) D
–3/2
–1/2 –4 2
–1/2 1
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1.7a - Absolute Value Inequalities

4. 1.7a - Absolute Value Inequalities
ABS VALUE
23.
Neither
25.
Parallel
26.
27.
29.
31.
33.
y = 21x – 40
35.
y = 1/6x + 4/3
37.
y = –3x – 8
38.
Park Place
13.
15.
m = 2/3
17.
19a.
20.
21.
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1.7a - Absolute Value Inequalities

5. 1.7a - Absolute Value Inequalities
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Absolute Value Inequalities
Section 1.7a
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1.7a - Absolute Value Inequalities

6. 1.7a - Absolute Value Inequalities
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Steps
Identify whether it is an AND/OR inequality
Write both equations with one with the regular sign and other equation with the sign SWITCHED with OPPOSITE number
Solve each inequality and write answer in inequality and/or interval notation
Check each solution and make sure there aren’t any extraneous solutions
Graph appropriately on number line 6
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1.7a - Absolute Value Inequalities

7. Solving Absolute Value Inequalities
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Solving Absolute Value Inequalities
When Solving for Inequalities, remember:
Less ThAND GreatOR Than
Less Than, “AND” Greater Than, “OR” 7
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1.7a - Absolute Value Inequalities

8. 1.7a - Absolute Value Inequalities
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Example 1
Solve |x + 3| < 5 and graph the solution on a number line. | 2 | –8 | 8
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1.7a - Absolute Value Inequalities

9. 1.7a - Absolute Value Inequalities
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Example 2
Solve |4x + 5| > 13 and graph the solution on a number line. | 2 |
–9/2 | 9
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1.7a - Absolute Value Inequalities

10. 1.7a - Absolute Value Inequalities
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Example 3
Solve |1/7x + 2| – 5 < 3 and graph the solution on a number line. | 42 |
–70 |
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1.7a - Absolute Value Inequalities

11. 1.7a - Absolute Value Inequalities
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YOUR TURN
Solve |2x – 5| > x + 1 and graph the solution on a number line. |
4/3 6
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1.7a - Absolute Value Inequalities

12. 1.7a - Absolute Value Inequalities
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Example 4
Solve 3|12 – 4x|+ 4 < 28 and graph the solution on a number line.
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1.7a - Absolute Value Inequalities

13. 1.7a - Absolute Value Inequalities
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Example 4
Solve 3|12 – 4x|+ 4 < 28 and graph the solution on a number line. | | 1 | 5
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1.7a - Absolute Value Inequalities

14. 1.7a - Absolute Value Inequalities
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Example 5
Solve 8|x + 4|> 48 and graph the solution on a number line. |
–10 | –2 |
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1.7a - Absolute Value Inequalities

15. 1.7a - Absolute Value Inequalities
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Example 6
Solve and graph the solution on a number line. | –8 | | 4
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1.7a - Absolute Value Inequalities

16. 1.7a - Absolute Value Inequalities
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YOUR TURN
Solve and graph the solution on a number line. | –8 | | 1
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1.7a - Absolute Value Inequalities

17. 1.7a - Absolute Value Inequalities
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Example 7
Solve |2x – 1| < –25 and graph the solution on a number line. |
No Solution
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1.7a - Absolute Value Inequalities

18. 1.7a - Absolute Value Inequalities
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Example 8
Solve |x + 1| > –16 and graph the solution on a number line. |
All Real Numbers
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1.7a - Absolute Value Inequalities

19. 1.7a - Absolute Value Inequalities
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Your Turn
Solve –2|x + 4| < 22 and graph the solution on a number line. |
No Solution
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1.7a - Absolute Value Inequalities

20. Absolute Value Applications
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Absolute Value Applications
To write the equation:
|actual amount – ideal amount| < tolerance
Tolerance is the max accepted deviation of an item from some ideal or mean
Tolerance = (High End) – (Avg of Low and High Ends)
If the problem is “within range,” apply < (AND), “acceptable”
If the problem is “out of range,” apply > (OR), “unacceptable”
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1.7a - Absolute Value Inequalities

21. 1.7a - Absolute Value Inequalities
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Example 9
A manufacturer has a 0.6oz tolerance for a bottle of salad dressing advertised as 16oz. Write and solve an absolute value inequality that describes the acceptable volumes for “16oz” bottles.
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1.7a - Absolute Value Inequalities

22. 1.7a - Absolute Value Inequalities
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Example 10
A manufacturer has a tolerance of 0.36 lb for a bag of potting soil advertised as 9.6 lb. Write and solve an absolute value inequality that describes unacceptable weights for “9.6 lb” bags.
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1.7a - Absolute Value Inequalities

23. 1.7a - Absolute Value Inequalities
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YOUR TURN
A food manufacture specifies that every family size box of cereal should have a net weight of 25 ounces, with a tolerance of 1.2 ounces. Write and solve an absolute value inequality that describes the acceptable net weights for the cereal in a family size box.
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1.7a - Absolute Value Inequalities

24. 1.7a - Absolute Value Inequalities
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Assignment
Worksheet
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1.7a - Absolute Value Inequalities