Solving & Graphing Absolute Value Chapter Problems
1. What types of real-life situations does solving absolute value equations and inequalities
apply?
2. What does the range between two numbers and absolute value have in common?
3. Distance is often used to explain absolute value. Why?
4. Why can’t the absolute value of a number have a negative value? How does this concept
apply to solving absolute value equations?
5.
Why does the graph of an absolute value equation have a “V” shape?
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Graphing & Absolute Value
Review
Classwork
1. │(-7)(-5)│ - │(2)(3)│
2. │-2│ + │(-3)2(-3)│ -1
3. -10 - │-3│
4. │-2│ + │5 - 6│
5. - │- 4│
6. │8-5 │ - │(2)(3)│
7. 15 + │-2│ + │(-1)2 │ +16
8. 17 + │-3│
9. │-9│ + │12 - 6│
10. - │-13│
11. 6 - │-10│
Homework
12. │(2)(5-8)│
13. │-5-2│
14. -│-8│
15. │-3+2│ - │(-2)(4)│
16. -2 + │-3│
17. │(12)(-8 - 3)│
18. │-15-12 + 7│
19. 4 -│-8│
20. │-13+21│ - │(-2)(4)2 │
21. -2 + │-3│- 21
22. -│-3+2│ + │(-2)(4) - 8│
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Absolute Value Equations
Classwork
How many solutions do these problems have?
23. │x│= 13
24. │-2x +6│= -6
Solve:
25. │3x+5│ +3 = 14
26. │4x-2│ = 0
27. Write an absolute value equation that has 1 and 5 as its solutions.
28. Write an absolute value equation that has -1 and 7 as its solutions.
Homework
How many solutions do these problems have?
29. │x+20│ = 0
30. │-3x+7| = 16
Solve:
31. │x+3│-4= 10
32. │-4x+7│= 20
33. Write an absolute value equation that has 0 and 4 as its solutions.
34. Write an absolute value equation that has -3 and 9 as its solutions.
Absolute Value Inequalities
Classwork
Solve:
35. │3x-10│ < -4
36. │2x+3│< 17
37. │-4x+7│>20
38. │x+20│ > 0
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39. |4b – 5| + 7 > 4
40. │(2)(5-8) + x │ > 13
Homework
Solve:
41. │x-2│+4 > 6
42. │x+6│ < 15
43. |5w + 3| - 4 > -9
44. │-3x+2│ < 8
45. │-x-3│ > 5
46. │3x+5│ < -4
Absolute Value Functions
Classwork
Graph
y = │x │+ 3
47.
48. y = │x - 1│
y
y
7
7
6
6
5
5
4
4
3
3
2
2
1
1
x
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
x
-7
-6
-5
-4
-3
-2
-1
1
-1
-1
-2
-2
-3
-3
-4
-4
-5
-5
-6
-6
-7
-7
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2
3
4
5
6
7
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y = │x │- 2
49.
50. y = │x + 2│
y
y
7
7
6
6
5
5
4
4
3
3
2
2
1
1
x
x
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
-7
7
-5
-4
-3
-2
-1
-1
-1
-2
-2
-3
-3
-4
-4
-5
-5
-6
-6
-7
-7
y = │x │
51.
-6
1
2
3
4
5
6
2
3
4
5
6
7
2
3
4
5
6
52. y = 2│x │ + 1
y
y
7
7
6
6
5
5
4
4
3
3
2
2
1
1
x
-7
-6
-5
-4
-3
-2
7
-1
1
2
3
4
5
6
x
7
-7
-6
-5
-4
-3
-2
-1
1
-1
-1
-2
-2
-3
-3
-4
-4
-5
-5
-6
-6
-7
-7
Homework
Graph
y = │x + 2│
53.
54. y = │x │ - 1
y
y
7
7
6
6
5
5
4
4
3
3
2
2
1
1
x
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
x
-7
-6
-5
-4
-3
-2
-1
1
-1
-1
-2
-2
-3
-3
-4
-4
-5
-5
-6
-6
-7
-7
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y = │x -2│
55.
56. y = │x │+ 4
y
y
7
7
6
6
5
5
4
4
3
3
2
2
1
1
x
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
x
7
-7
-5
-4
-3
-2
-1
1
-1
-1
-2
-2
-3
-3
-4
-4
-5
-5
-6
-6
-7
-7
y = │x │ - 4
57.
-6
2
3
4
5
6
3
4
5
6
7
58. y = 2│x - 1│
y
y
7
7
6
6
5
5
4
4
3
3
2
2
1
1
x
-7
-6
-5
-4
-3
-2
-1
7
1
2
3
4
5
6
7
x
-7
-6
-5
-4
-3
-2
-1
1
-1
-1
-2
-2
-3
-3
-4
-4
-5
-5
-6
-6
-7
-7
2
Chapter Review
Multiple Choice– Choose the correct answer for each question.
1. The expression 7––7 is equivalent to
a.
b.
c.
d.
-7
0
7
14
2.
-│5-6│+│(-3)(-2)│
a. -5
b. 5
c. 7
d. -7
3.
│(3)(-4)│ + │(5)(-3)│
a. 3
b. -3
c. 27
d. -27
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4.
│15-10│ + │(-2)2 -1│
a. -5
b. 5
c. 8
d. -8
5.
How many solutions does │x│= -2 have?
a. One
b. Two
c. No Solution
d. Infinitely Many Solutions
6.
│5x+12│= 13
a. x =
1
5
b. x = -5,
c.
1
5
x = 5, -5
d. x = 5,
1
5
7.
│-2x - 3│= 29
a. x = -16
b. x = 13
c. x =16, -13
d. x = -16, 13
8.
Write an absolute value equation with the solutions 5 and-7 as its solutions.
a. | x – 1 | = 4
b. | x – 1 | = - 6
c. | x – 1 | = 6
d. | x + 1 | = 6
9.
│-3x + 5│> 10
5
or x > 5
3
5
b. x < and x > 5
3
5
c. x > or x < 5
3
5
d. x < or x < 5
3
a. x < -
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10. │2x+ 5│< 13
a. -9 < x < 4
b. – 9 > x > 4
c.
- 9< x or x < 4
d. – 9 < x < - 4
11. │- 2x - 10│< 6
a. x ≥ -8 and x ≥ -2
b.
x ≥ -8 and x ≤ -2
c.
x ≤ -8 and x ≥ -2
d.
x ≥ -8
12. The equation for the graphed function is:
a.
y = │x + 4 │
b.
y=│x–4│
c.
y = │x │+ 4
d.
y = │x │ - 4
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13. a. y = │x + 2 │
b. y = │x │ + 2
c. y = │x – 2 │
d. y = │x │ - 2
Short Constructed Response – Write the correct answer for each question.
14. │4x + 7│- 3 = 12
15.
-2 + │-2x - 1│ = 31
16.
Write an absolute value equation that has -1 and 4 as its solutions.
17.
The graph of y = │x - 5│, is simply the graph of y = │x │translated ____________.
Extended Constructed Response - Solve the problem, showing all work.
18. Solve:
a. 3 + │-5x - 5│ < 48
b.
3 + │-5x - 5│ > 48
c.
Are the solutions the same or different for part a & b? Explain your answer.
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Answers
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
29
28
-13
3
-4
-3
34
20
15
-13
-4
6
7
-8
-7
1
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
132
20
-4
-24
-20
15
2
None
x = 2, -16/3
x=½
|𝑥 − 3|= 2
|𝑥 − 3| = 4
1
2
X = 11, -17
x = -13/4, 27/4
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
44.
45.
46.
|𝑥 − 2|= 2
|𝑥 − 3|= 6
No solution
-10 < x < 7
x < -13/4 or x >
27/4
All real numbers
All real numbers
x ≤ - 7 or x ≥ 19
x < 0 or x > 4
All real numbers
All real numbers
x > -2 and x < 10/3
x ≤ - 8 or x ≥ 2
No solution
47. 𝑦 = |𝑥| + 3
48. 𝑦 = |𝑥 − 1|
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49. 𝑦 = |𝑥| − 2
50. 𝑦 = |𝑥 + 2|
51. 𝑦 = |𝑥|
52. 𝑦 = 2|𝑥| + 1
53. 𝑦 = |𝑥 + 2|
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54. 𝑦 = |𝑥| − 1
55. 𝑦 = |𝑥 − 2|
56. 𝑦 = |𝑥| + 4
57. 𝑦 = |𝑥| − 4
58. 𝑦 = 2|𝑥 − 1|
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Chapter Review
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
B
B.
C
C
C
B
D
D
A
A
B
B
B
x = -2, -11/2
x = 16, -17
3
5
|𝑥 − |=
2
2
5 units to the right
A. x > -10 and x < 8
B. x < -10 or x > 8
C. They are different solutions
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