Absolute Value Equations
|x| = 3
{3, -3}
| a + 3 | < 5
What is a > -8 and a < 2
6 | g - 3 | = 42
What is { 10 , -4 }
4| 8x - 2 | - 5 < 19
What is x < 1 and x > -1/2
-1/2 <x < 1
|3 + n| < 7
What is n > -10 and n < 4
-10 < n < 4
| z - 13 | = 21
What is { -8 , 34 }
3 | r - 4 | = 21
What is { -3 , 11 }
8 |4m + 1| < -80
(hint: be careful after isolating the absolute value)
No Solutions (the absolute value has to be positive)
6 + 7|x + 1| ≥ -1
What is x ≥ -2 or x ≤ 0
All Real Numbers ;)
| p + 1 | + 10 = 5
What is No Solution
3 | 2a - 4 | = 0
What is { 2 }
2| 8k - 10 | - 1 > 75
What is k > 6 or k < -7/2
-3| 10 + x | ≥ 12
(Hint: Be careful after isolating absolute value)
No solutions
5 | q + 6 | = 20
What is { -2 , -10 }
Graph the following inequality
| x – 9| ≤ 17
What is x ≥ -8 and x ≤ 26
-8 ≤ x ≤ 26
2 | y + 4 | = 14
What is { 3 , -11 }
10| 4x – 1 | - 7 ≤ 103
What is x ≤ 3 and x ≥ -5/2
-5/2 ≤ x ≤ 3
Graph the following inequality
9 + 10 | a – 1 | ≥ 29
What is a ≤ -1 or a ≥ 3
| 3n + 18| = 6n
One solution n = 6
Reject n = -2 because it is extraneous (doesn't satisfy the original equation).
| -b + 5| ≤ -16
No Solution
5 - 9| 9 - k| = -13
{7 , 11}
1 – 3| -9n – 10 | ≥ -2
What is n ≤ -1 and n ≥ -11/9
-11/9 ≤ n ≤ -1
Graph the following inequality
-2| 4t + 3 | < 40
(Hint: be careful after isolating absolute value)
This will not be on the assessment
Infinite Solutions (All Real Numbers)