3.1 a) x = 6 / 5 or x = 2, b) x = - 3 / 2 or x = - 1 / 4, c) x = - 3 or x = 2, d) x = 1 or x = - 2.
3.2 a) x = 9 or x = - 3, b) x = 1 or x = - 1 / 4, c) x = - 3 or x = - 5 d) x = 8 or x = - 18
<h3>How to solve algebraic problems by appying absolute value properties</h3>
In this question we have eight expressions involving <em>absolute value</em> expressions, which can be solved by using the following procedure:
3.1 a) |(1 / 2) · x| = 3 - 2 · x
For x ≥ 0:
(1 / 2) · x = 3 - 2 · x
(5 / 2) · x = 3
x = 6 / 5
For x < 0:
- (1 / 2) · x = 3 - 2 · x
(3 / 2) · x = 3
x = 2
b) |x - 1| = 3 · x + 2
For x ≥ 1:
x - 1 = 3 · x + 2
2 · x = - 3
x = - 3 / 2
For x < 1:
- x + 1 = 3 · x + 2
4 · x = - 1
x = - 1 / 4
c) |5 · x| = x - 12
For x ≥ 0:
5 · x = x - 12
4 · x = - 12
x = - 3
For x < 0:
- 5 · x = x - 12
6 · x = 12
x = 2
d) |7 - x| = 5 · x + 1
For x ≤ 7:
7 - x = 5 · x + 1
6 · x = 6
x = 1
For x > 7:
x - 7 = 5 · x + 1
4 · x = - 8
x = - 2
3.2 a) |9 + x| = 2 · x
For x ≥ - 9:
9 + x = 2 · x
x = 9
For x < 9:
- 9 - x = 2 · x
3 · x = - 9
x = - 3
b) |5 · x| - 3 · x = 2
For x ≥ 0:
|5 · x| = 2 + 3 · x
5 · x = 2 + 3 · x
2 · x = 2
x = 1
For x < 0:
- 5 · x = 2 + 3 · x
- 8 · x = 2
x = - 1 / 4
c) |x + 6| - 9 = 2 · x
For x ≥ - 6:
x + 6 - 9 = 2 · x
x - 3 = 2 · x
x = - 3
For x < - 6:
- x - 6 - 9 = 2 · x
- x - 15 = 2 · x
3 · x = - 15
x = - 5
d) |2 · x - 3| + x = 21
For x ≥ 3 / 2:
2 · x - 3 + x = 21
3 · x = 24
x = 8
For x < 3 / 2:
- 2 · x + 3 + x = 21
- x = 18
x = - 18
To learn more on absolute values: brainly.com/question/1301718
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