Question

select all of the equations below that are equivalent to 13 = m + 6

15 = m + 6 + 2
15 = 4 + m + 6
18 = 5 + m + 6
13 + 12 = m + 20

Answer 1

To determine which equations are equivalent to the equation \( 13 = m + 6 \), we can manipulate that equation to find the value of \( m \):

1. Rearranging, we find:
\[
m = 13 - 6
\]
\[
m = 7
\]

Now we can check each of the given equations by substituting \( m \) with \( 7 \):

1. **Equation:** \( 15 = m + 6 + 2 \)
- Substitute \( m = 7 \):
\[
15 = 7 + 6 + 2 \\
15 = 15 \quad \text{(True)}
\]

2. **Equation:** \( 15 = 4 + m + 6 \)
- Substitute \( m = 7 \):
\[
15 = 4 + 7 + 6 \\
15 = 17 \quad \text{(False)}
\]

3. **Equation:** \( 18 = 5 + m + 6 \)
- Substitute \( m = 7 \):
\[
18 = 5 + 7 + 6 \\
18 = 18 \quad \text{(True)}
\]

4. **Equation:** \( 13 + 12 = m + 20 \)
- Substitute \( m = 7 \):
\[
13 + 12 = 7 + 20 \\
25 = 27 \quad \text{(False)}
\]

Thus, the equations equivalent to \( 13 = m + 6 \) are:

- \( 15 = m + 6 + 2 \)
- \( 18 = 5 + m + 6 \)

So the correct choices are:

- \( 15 = m + 6 + 2 \)
- \( 18 = 5 + m + 6 \)