Question

Solve the equation. Check your answer.
negative 3 left parenthesis r plus 8 right parenthesis equals negative 49

Answer 1

To solve the equation \(-3(r + 8) = -49\), we can follow these steps:

1. Divide both sides by -3 to isolate the term inside the parentheses:

\[
r + 8 = \frac{-49}{-3}
\]

This simplifies to:

\[
r + 8 = \frac{49}{3}
\]

2. Next, subtract 8 from both sides to solve for \(r\):

\[
r = \frac{49}{3} - 8
\]

Since \(8\) can be expressed as a fraction with a denominator of \(3\):

\[
8 = \frac{24}{3}
\]

So,

\[
r = \frac{49}{3} - \frac{24}{3} = \frac{49 - 24}{3} = \frac{25}{3}
\]

Thus, we find:

\[
r = \frac{25}{3}
\]

### Checking the solution

To check if our solution is correct, we can substitute \(r = \frac{25}{3}\) back into the original equation:

1. Substitute \(r\) into \(r + 8\):

\[
r + 8 = \frac{25}{3} + 8 = \frac{25}{3} + \frac{24}{3} = \frac{49}{3}
\]

2. Then we multiply by \(-3\):

\[
-3(r + 8) = -3 \left( \frac{49}{3} \right) = -49
\]

Since both sides of the equation are equal, our solution is verified.

The final answer is:

\[
r = \frac{25}{3}
\]