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The equation you provided is:

\[
|-2m + 10| = 10
\]

To solve this absolute value equation, we will break it into two cases:

### Case 1: The expression inside the absolute value is positive or zero
\[
-2m + 10 = 10
\]
Solve for \( m \):
\[
-2m = 10 - 10 = 0
\]
\[
m = 0
\]

### Case 2: The expression inside the absolute value is negative
\[
-(-2m + 10) = 10
\]
Simplify:
\[
2m - 10 = 10
\]
Solve for \( m \):
\[
2m = 10 + 10 = 20
\]
\[
m = \frac{20}{2} = 10
\]

### Final Solutions:
The solutions are \( m = 0 \) and \( m = 10 \).

Would you like further details or have any questions? Here are 5 related questions to expand this topic:

1. How do you solve absolute value inequalities?
2. What are the general rules for solving absolute value equations?
3. How can you check if your solutions are correct in an absolute value equation?
4. What are the key differences between solving absolute value equations and inequalities?
5. Can absolute value equations have no solution?

**Tip**: Always check both cases when solving absolute value equations, as it represents both positive and negative scenarios.

Learn how to solve the absolute value equation |-2m + 10| = 10 with a step-by-step solution. This problem covers key algebraic concepts, including absolute value properties and solving two cases. Suitable for students in Grades 8-10.

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