Question

1/5 (10 - 5q) - 3 = q use multiplication as your first step

Answer 1

To solve the equation \( \frac{1}{5} (10 - 5q) - 3 = q \) using multiplication as the first step, we can multiply both sides of the equation by 5 to eliminate the fraction.

Starting with the equation:

\[
\frac{1}{5} (10 - 5q) - 3 = q
\]

Multiply both sides by 5:

\[
5 \left( \frac{1}{5} (10 - 5q) - 3 \right) = 5q
\]

This simplifies to:

\[
10 - 5q - 15 = 5q
\]

Now, combine like terms on the left side:

\[
10 - 15 - 5q = 5q
\]

This further simplifies to:

\[
-5 - 5q = 5q
\]

Next, add \(5q\) to both sides to isolate the terms with \(q\):

\[
-5 = 5q + 5q
\]

This simplifies to:

\[
-5 = 10q
\]

Now, divide both sides by 10:

\[
q = \frac{-5}{10}
\]

Simplifying gives us:

\[
q = -\frac{1}{2}
\]

So, the solution is:

\[
q = -\frac{1}{2}
\]