Answer:
x = - 16 , x = 24
Step-by-step explanation:
Given
f(x) = 0.5| x - 4 | - 3 and f(x) = 7, then equating gives
0.5|x - 4 | - 3 = 7 ( add 3 to both sides )
0.5| x - 4 | = 10 ( divide both sides by 0.5 )
| x - 4 | = 20
The expression inside the absolute value can be positive or negative, that is
x - 4 = 20 or - (x - 4) = 20
solving both
x - 4 = 20 ( add 4 to both sides )
x = 24
or
- (x - 4) = 20
- x + 4 = 20 ( subtract 4 from both sides )
- x = 16 ( multiply both sides by - 1 )
x = - 16
