Question

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Part 1
Solve the equation. Check your answer.
negative 5 left parenthesis r plus 2 right parenthesis equals negative 61

Answer 1

To solve the equation \(-5(r + 2) = -61\), we can follow these steps:

1. **Distribute \(-5\) on the left side**:
\[
-5r - 10 = -61
\]

2. **Add \(10\) to both sides**:
\[
-5r - 10 + 10 = -61 + 10
\]
\[
-5r = -51
\]

3. **Divide by \(-5\)** to isolate \(r\):
\[
r = \frac{-51}{-5} = \frac{51}{5} = 10.2
\]

### Check the solution:

Substituting \(r = 10.2\) back into the original equation:

\[
-5(10.2 + 2) = -61
\]
First, calculate \(10.2 + 2\):
\[
10.2 + 2 = 12.2
\]
Now, calculate \(-5 \times 12.2\):
\[
-5 \times 12.2 = -61
\]

Both sides of the equation are equal, confirming that the solution is correct.

Thus, the solution is:
\[
r = 10.2
\]