Let's solve the equation step by step:

\[
2m - 13 = -8m + 27
\]

1. **Add \(8m\) to both sides** to move all terms with \(m\) to one side:

\[
2m + 8m - 13 = 27
\]

This simplifies to:

\[
10m - 13 = 27
\]

2. **Add 13 to both sides** to isolate the term with \(m\):

\[
10m - 13 + 13 = 27 + 13
\]

This simplifies to:

\[
10m = 40
\]

3. **Divide both sides by 10** to solve for \(m\):

\[
m = \frac{40}{10} = 4
\]

So, the solution is:

\[
m = 4
\]

Would you like more details or have any questions about this solution?

Here are five related questions:
1. What would the solution be if the equation was \(3m - 13 = -8m + 27\)?
2. How would you solve the equation \(2m - 13 = 5m + 27\)?
3. What happens if we subtract \(27\) from both sides of the original equation?
4. Can you solve the equation \(2m - 13 = 2(-8m + 27)\)?
5. How do you solve for \(m\) if you had \(2m - 13 = -4m + 27\)?

**Tip:** When solving linear equations, always start by moving all terms involving the variable to one side of the equation.

Learn how to solve the equation 2m - 13 = -8m + 27 with a detailed step-by-step solution. This problem involves linear equations and covers basic algebraic concepts. Suitable for students in Grades 7-9.

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