Answer:
x = 3, x = 4
Step-by-step explanation:
The absolute value function always gives a positive result.
However the expression inside can be positive or negative, that is
2x - 7 = 1 or - (2x - 7) = 1
solving both
2x - 7 = 1 ( add 7 to both sides )
2x = 8 ( divide both sides by 2 )
x = 4
or
- (2x - 7) = 1 ← distribute left side
- 2x + 7 = 1 ( subtract 7 from both sides )
- 2x = - 6 ( divide both sides by - 2 )
x = 3
As a check
Substitute these values into the left side of the equation and if equal to the right side then they are the solutions.
x = 4 : | 8 - 7 | = | 1 | = 1 = right side
x = 3 : | 6 - 7 | = | - 1 | = 1 = right side
Then x = 3, x = 4 are the solutions
