|x+1| + |2x-5|=0

To solve the equation |x+1|+|2x-5|=0, we need to find the values of x that make the equation true.

Since the absolute value of any number is always non-negative, the sum of two absolute values can only be zero if both absolute values are zero.

So, we need to solve the two equations separately:

1. x + 1 = 0
Subtract 1 from both sides:
x = -1

2. 2x - 5 = 0
Add 5 to both sides:
2x = 5
Divide both sides by 2:
x = 5/2

Therefore, the solutions to the equation |x+1|+|2x-5|=0 are x = -1 and x = 5/2.