Question

select the equations below that are equivalent to 12 - r = 6

18 - r = 6 + 6
14 - r = 2 + 6
12 - r + 13 = 19
13 - r = 3 + 6

Answer 1

To determine which equations are equivalent to \( 12 - r = 6 \), we'll simplify each of the given equations and see if they result in the same form.

1. **Equation 1:** \( 18 - r = 6 + 6 \)

Simplifying the right side:
\[
18 - r = 12
\]
Rearranging gives:
\[
-r = 12 - 18
\]
\[
-r = -6
\]
\[
r = 6
\]

2. **Equation 2:** \( 14 - r = 2 + 6 \)

Simplifying the right side:
\[
14 - r = 8
\]
Rearranging gives:
\[
-r = 8 - 14
\]
\[
-r = -6
\]
\[
r = 6
\]

3. **Equation 3:** \( 12 - r + 13 = 19 \)

Simplifying the left side:
\[
25 - r = 19
\]
Rearranging gives:
\[
-r = 19 - 25
\]
\[
-r = -6
\]
\[
r = 6
\]

4. **Equation 4:** \( 13 - r = 3 + 6 \)

Simplifying the right side:
\[
13 - r = 9
\]
Rearranging gives:
\[
-r = 9 - 13
\]
\[
-r = -4
\]
\[
r = 4
\]

From all the equations:

- The first three equations (1, 2, and 3) lead to \( r = 6 \), which is consistent with the original equation \( 12 - r = 6 \).
- The fourth equation leads to \( r = 4 \), which is not equivalent.

Thus, the equations equivalent to \( 12 - r = 6 \) are:

- \( 18 - r = 6 + 6 \)
- \( 14 - r = 2 + 6 \)
- \( 12 - r + 13 = 19 \)