To solve this equation, we have to consider two cases when the absolute value expressions are positive and when they are negative.
Case 1: When both expressions are positiveWe have:2x - 5 - (4 - x) = -182x - 5 - 4 + x = -183x - 9 = -183x = -9x = -3
Case 2: When both expressions are negativeWe have:-(2x - 5) - (-(4 - x)) = -18-2x + 5 - 4 + x = -18-x + 1 = -18-x = -19x = 19
Therefore, the solutions to the equation are x = -3 and x = 19.
To solve this equation, we have to consider two cases when the absolute value expressions are positive and when they are negative.
Case 1: When both expressions are positive
We have:
2x - 5 - (4 - x) = -18
2x - 5 - 4 + x = -18
3x - 9 = -18
3x = -9
x = -3
Case 2: When both expressions are negative
We have:
-(2x - 5) - (-(4 - x)) = -18
-2x + 5 - 4 + x = -18
-x + 1 = -18
-x = -19
x = 19
Therefore, the solutions to the equation are x = -3 and x = 19.