Answer:
x = 1
Step-by-step explanation:
The absolute value always gives a positive value. However, the expression inside can be positive or negative , so
4x - 13 = 5x + 4 ( subtract 4x from both sides )
- 13 = x + 4 ( subtract 4 from both sides )
- 17 = x
OR
- (4x - 13) = 5x + 4 , simplify left side
- 4x + 13 = 5x + 4 ( subtract 5x from both sides )
- 9x + 13 = 4 ( subtract 13 from both sides )
- 9x = - 9 ( divide both sides by - 9 )
x = 1
As a check
Substitute these values into the equation and if both sides are equal then they are solutions.
x = - 17
left side = | 4(- 17) - 13 | = | - 68 - 13 | = | - 81 | = 81
right side = 5(- 17) + 4 = - 85 + 4 = - 81 ≠ 81
Then x = - 17 is an extraneous solution
x = 1
left side = | 4(1) - 13 | = | 4 - 13 | = | - 9 | = 9
right side = 5(1) + 4 = 5 + 4 = 9
Then solution is x = 1
