Question

Solve the equation and check your solution.



2m−13=−8m+27

Answer 1

To solve the equation \( 2m - 13 = -8m + 27 \), we first want to isolate the variable \( m \).

1. **Add \( 8m \) to both sides:**

\[
2m + 8m - 13 = 27
\]
This simplifies to:
\[
10m - 13 = 27
\]

2. **Add \( 13 \) to both sides:**

\[
10m - 13 + 13 = 27 + 13
\]
This simplifies to:
\[
10m = 40
\]

3. **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:

\[
\boxed{4}
\]