Answer:
x = - 3 , x = 21
Explanation:
given the absolute value equation
- 1 + |- 9 + x | = 11 ( add 1 to both sides )
| - 9 + x | = 12
the absolute value function , always gives a positive result, however the expression inside the bars can be positive or negative.
there are then 2 equations to be solved
- 9 + x = 12 or - (- 9 + x) = 12
- 9 + x = 12 ( add 9 to both sides )
x = 21
or
- (- 9 + x) = 12 ← distribute parenthesis by - 1
9 - x = 12 ( subtract 9 from both sides )
- x = 3 ( multiply both sides by - 1 )
x = - 3
solutions are x = - 3 , x = 21