Answer:
x = - 1 , x = 5
Explanation:
- | x - 2 | + 3 = 0 ( subtract 3 from both sides )
- | x - 2 | = - 3 ( divide both sides by - 1 )
| x - 2 | = 3
the absolute value always gives a positive value, however, the expression inside the bars can be positive or negative, then
x - 2 = 3 or - (x - 2) = 3 ( solve both equations )
x - 2 = 3 ( add 2 to both sides )
x = 5
or
- (x - 2) = 3
- x + 2 = 3 ( subtract 2 from both sides )
- x = 1 ( multiply both sides by - 1 )
x = - 1
As a check
substitute these values into the equation and if both sides are equal then it is a solution.
x = - 1
left side = - | - 1 - 2 | + 3 = - | - 3 | + 3 = - | 3 | + 3 = - 3 + 3 = 0 = right side
x = 5
left side = - | 5 - 2 | + 3 = - | 3 | + 3 = - 3 + 3 = 0 = right side
solutions are x = - 1 , x = 5