Question

All of the following equations have the same solution except _____.

-10 = -3 m + 2
3 m + 2 = -10
2 - 3 m = -10
-3 m + 2 = -10

Answer 1

Let's solve each equation to find their solutions.

1. **Equation 1:** \(-10 = -3m + 2\)

Rearranging gives:
\[
-3m = -10 - 2
\]
\[
-3m = -12
\]
\[
m = \frac{-12}{-3} = 4
\]

2. **Equation 2:** \(3m + 2 = -10\)

Rearranging gives:
\[
3m = -10 - 2
\]
\[
3m = -12
\]
\[
m = \frac{-12}{3} = -4
\]

3. **Equation 3:** \(2 - 3m = -10\)

Rearranging gives:
\[
-3m = -10 - 2
\]
\[
-3m = -12
\]
\[
m = \frac{-12}{-3} = 4
\]

4. **Equation 4:** \(-3m + 2 = -10\)

Rearranging gives:
\[
-3m = -10 - 2
\]
\[
-3m = -12
\]
\[
m = \frac{-12}{-3} = 4
\]

Now we can summarize the solutions:
- Equation 1: \(m = 4\)
- Equation 2: \(m = -4\)
- Equation 3: \(m = 4\)
- Equation 4: \(m = 4\)

All equations have the same solution except for **Equation 2**, which has \(m = -4\).

Therefore, the answer is \(\boxed{2}\).