Question

Fill in the blank question.
Solve the equation. Check your solution.



−5(−a−1)=3a−7

Answer 1

To solve the equation \(-5(-a - 1) = 3a - 7\), let's start by distributing \(-5\) on the left side.

\[
-5(-a - 1) = 5a + 5
\]

Now we rewrite the equation:

\[
5a + 5 = 3a - 7
\]

Next, we can move the \(3a\) from the right side to the left side by subtracting \(3a\) from both sides:

\[
5a - 3a + 5 = -7
\]

This simplifies to:

\[
2a + 5 = -7
\]

Now, let's isolate \(2a\) by subtracting \(5\) from both sides:

\[
2a = -7 - 5
\]

This gives us:

\[
2a = -12
\]

Next, we can solve for \(a\) by dividing both sides by \(2\):

\[
a = \frac{-12}{2} = -6
\]

Thus, the solution is:

\[
\boxed{-6}
\]

Now, we will check our solution by substituting \(a = -6\) back into the original equation:

Starting with the left side:

\[
-5(-(-6) - 1) = -5(6 - 1) = -5(5) = -25
\]

Now for the right side:

\[
3(-6) - 7 = -18 - 7 = -25
\]

Since both sides equal \(-25\), our solution checks out:

\[
\text{Both sides are equal: } -25 = -25
\]

Thus, the solution \(a = -6\) is verified.