We are given the absolute value equation:

$|2x - 5| + 10 = 5$

Step 1: Isolate the absolute value expression

Subtract 10 from both sides:

$|2x - 5| = 5 - 10$ $|2x - 5| = -5$

Step 2: Analyze the equation

Since the absolute value of any expression is always non-negative (i.e., it must be greater than or equal to 0), there is no solution when the absolute value equals a negative number.

Thus, there is no solution to the equation.

Would you like more details, or do you have any questions?

Related Questions:

1. How do you solve absolute value inequalities?
2. Can absolute value equations have no solution?
3. What if the equation were $|2x - 5| = 5$?
4. How do absolute value functions affect graphing?
5. What are the steps for solving more complex absolute value equations?

Tip:

Always check if isolating the absolute value leads to a negative number—if it does, the equation has no solution.