Question

Question
Solve for x in the equation 8/11(x+4/5)=24/55 .(1 point)

Answer 1

To solve the equation \( \frac{8}{11}(x + \frac{4}{5}) = \frac{24}{55} \), we will first eliminate the fraction by multiplying both sides by the least common multiple (LCM) of the denominators. The LCM of 11 and 55 is 55.

1. Multiply both sides by 55:

\[
55 \cdot \frac{8}{11}(x + \frac{4}{5}) = 55 \cdot \frac{24}{55}
\]

2. Simplify the left side:

\[
5 \cdot 8(x + \frac{4}{5}) = 24
\]

\[
40(x + \frac{4}{5}) = 24
\]

3. Divide both sides by 40:

\[
x + \frac{4}{5} = \frac{24}{40}
\]

4. Simplify the fraction on the right:

\[
\frac{24}{40} = \frac{3}{5}
\]

Thus, we have:

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

5. Subtract \(\frac{4}{5}\) from both sides:

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

6. This simplifies to:

\[
x = -\frac{1}{5}
\]

So, the solution is:

\[
\boxed{-\frac{1}{5}}
\]