absolute value problem
|2x - 1| - |x + 5| = 3.

Answer is -7/3, 9

The expressions inside the absolute value terms will change sign at x = 1/2 for the first and x = -5 for the second.

For -5 < x < 1/2
-(2x - 1) - (x + 5) = 3 ----> -3x - 4 = 3 ----> -3x = 7 ----> x = -7/3

For x > 1/2
(2x - 1) - (x + 5) = 3 ----> x - 6 = 3 ----> x = 9

For x < -5
-(2x - 1) + (x + 5) = 3 ----> -x + 6 = 3 ----> x = 3
but this disagrees with the constraint.

Solution x = 9 or -7/3