|2x-3|=5

Absolute value

x = 4, x = - 1

Step-by-step explanation:

The absolute value always gives a positive result, however, the expression inside can be positive or negative, that is

2x - 3 = 5 or - (2x - 3) = 5

Solving both

2x - 3 = 5 ( add 3 to both sides )

2x = 8 ( divide both sides by 2 )

x = 4

or

- (2x - 3) = 5

- 2x + 3 = 5 ( subtract 3 from both sides )

- 2x = 2 ( divide both sides by - 2 )

x = - 1

As a check

| 2(4) - 3 | = | 8 - 3 | = | 5 | = 5 ← True

| 2(- 1) - 3 | = | - 2 - 3 | = | - 5 | = 5 ← True

Thus the solutions are x = 4, x = - 1