Answer:
x = - 3, x = 9
Step-by-step explanation:
Given
2| x - 3 | - 5 = 7 ( add 5 to both sides )
2|x - 3 | = 12 ( divide both sides by 2 )
| x - 3 | = 6
The absolute value function always gives a positive value, however, the expression inside the bars can be positive or negative, that is
x - 3 = 6 or - (x - 3) = 6
Solving both equations
x - 3 = 6 ( add 3 to both sides )
x = 9
or
- (x - 3) = 6
- x + 3 = 6 ( subtract 3 from both sides )
- x = 3 ( multiply both sides by - 1 )
x = - 3
As a check
2|9 - 3| - 5 = 2|6| - 5 = 12 - 5 = 7 ← Correct
or
2|- 3 - 3| - 5 = 2|- 6| - 5 = 2 |6| - 5 = 12 - 5 = 7 ← Correct
Thus the solutions are x = - 3, x = 9
