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