Question

Please help me solve this problem

Answer 1

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

How to solve algebraic problems by appying absolute value properties

In this question we have eight expressions involving absolute value 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

#SPJ1