To solve the equation \( 2m - 13 = -8m + 27 \), we first want to isolate the variable \( m \).
- Add \( 8m \) to both sides:
\[ 2m + 8m - 13 = 27 \] This simplifies to: \[ 10m - 13 = 27 \]
- Add \( 13 \) to both sides:
\[ 10m - 13 + 13 = 27 + 13 \] This simplifies to: \[ 10m = 40 \]
- Divide both sides by \( 10 \):
\[ m = \frac{40}{10} \] This simplifies to: \[ m = 4 \]
Now we can check the solution by substituting \( m = 4 \) back into the original equation:
Original equation:
\[ 2m - 13 = -8m + 27 \]
Substituting \( m = 4 \):
Left side:
\[ 2(4) - 13 = 8 - 13 = -5 \]
Right side:
\[ -8(4) + 27 = -32 + 27 = -5 \]
Since both sides of the equation equal \(-5\), the solution is verified.
Thus, the solution is:
\[ \boxed{4} \]