Answer:
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
