Answer:
x = - 7 or x = 10
Step-by-step explanation:
The absolute value always returns a positive value, but the expression inside the bars can be positive or negative.
Given
| 2x - 3 | = 17, then
2x - 3 = 17 ( add 3 to both sides )
2x = 20 ( divide both sides by 2 )
x = 10
OR
- (2x - 3) = 17 ← distribute left side by - 1
- 2x + 3 = 17 ( subtract 3 from both sides )
- 2x = 14 ( divide both sides by - 2 )
x = - 7
As a check, substitute these values into the left side of the equation and if equal to the right side then they are the solutions
x = - 7 → | - 14 - 3 | = | - 17 | = 17 ← True
x = 10 → | 20 - 3 | = | 17 | = 17 ← True
Hence solutions are x = - 7 or x = 10
