Question

Which value of x satisfies the equation start fraction, 3, divided by, 5, end fraction, left parenthesis, x, minus, start fraction, 2, divided by, 5, end fraction, right parenthesis, equals, minus, start fraction, 141, divided by, 25, end fraction
5
3
​
(x−
5
2
​
)=−
25
141
​
?
Answer
Multiple Choice Answers
9
10
minus, 9
minus, 10

Answer 1

We start with the equation

\[
\frac{3}{5} \left( x - \frac{2}{5} \right) = -\frac{141}{25}.
\]

To eliminate the fraction on the left side, we can multiply both sides of the equation by \(5\):

\[
3 \left( x - \frac{2}{5} \right) = -\frac{141}{25} \times 5.
\]

Calculating the right side gives us:

\[
-\frac{141}{25} \times 5 = -\frac{141 \times 5}{25} = -\frac{705}{25} = -28.2.
\]

Now we have:

\[
3 \left( x - \frac{2}{5} \right) = -28.2.
\]

Next, divide both sides by 3:

\[
x - \frac{2}{5} = -\frac{28.2}{3}.
\]

Calculating \(-\frac{28.2}{3}\) gives us:

\[
-\frac{28.2}{3} \approx -9.4.
\]

Now, we can rewrite the equation:

\[
x - \frac{2}{5} = -9.4.
\]

To isolate \(x\), add \(\frac{2}{5}\) to both sides:

\[
x = -9.4 + \frac{2}{5}.
\]

First, we convert \(-9.4\) to a fraction. This equals \(-\frac{94}{10}\) or \(-\frac{47}{5}\) in simplified form. We can now proceed with the addition:

\[
x = -\frac{47}{5} + \frac{2}{5}.
\]

Combine the fractions:

\[
x = \frac{-47 + 2}{5} = \frac{-45}{5} = -9.
\]

Therefore, the value of \(x\) that satisfies the equation is

\[
\boxed{-9}.
\]

Among the multiple choice answers provided, the correct answer is **minus 9**.