Question

Solve 2/5(-5x+2)+3x-3=39
Leave your answer in simplified fraction form.

Answer 1

To solve the equation \( \frac{2}{5}(-5x + 2) + 3x - 3 = 39 \), we first distribute \( \frac{2}{5} \) on the left side:

\[
\frac{2}{5}(-5x) + \frac{2}{5}(2) + 3x - 3 = 39
\]

Calculating the distribution:

\[
\frac{2}{5} \cdot -5x = -2x \quad \text{and} \quad \frac{2}{5} \cdot 2 = \frac{4}{5}
\]

Thus, the equation simplifies to:

\[
-2x + \frac{4}{5} + 3x - 3 = 39
\]

Now combine like terms, starting with the \( x \) terms:

\[
-2x + 3x = x
\]

Next, combine the constant terms \( \frac{4}{5} \) and \(-3\). To combine these, we can rewrite \(-3\) in terms of fifths:

\[
-3 = -\frac{15}{5}
\]

Now we can combine \( \frac{4}{5} - \frac{15}{5} \):

\[
\frac{4}{5} - \frac{15}{5} = \frac{4 - 15}{5} = \frac{-11}{5}
\]

Now, our equation becomes:

\[
x - \frac{11}{5} = 39
\]

To isolate \( x \), add \( \frac{11}{5} \) to both sides:

\[
x = 39 + \frac{11}{5}
\]

To add \( 39 \) and \( \frac{11}{5} \), we convert \( 39 \) into a fraction with a denominator of \( 5 \):

\[
39 = \frac{195}{5}
\]

Now, add the fractions:

\[
x = \frac{195}{5} + \frac{11}{5} = \frac{195 + 11}{5} = \frac{206}{5}
\]

Thus, the solution in simplified fraction form is:

\[
\boxed{\frac{206}{5}}
\]