Let’s solve the equation step by step to see if your solution of \( x = \frac{13}{15} \) is correct.
The equation is:
\[ \frac{8}{11}(x + \frac{4}{5}) = \frac{24}{55} \]
To eliminate the fraction, we can first multiply both sides of the equation by \( 11 \) to get rid of the \( \frac{8}{11} \):
\[ 8(x + \frac{4}{5}) = \frac{24}{55} \cdot 11 \]
Calculate \( \frac{24}{55} \cdot 11 \):
\[ \frac{24 \cdot 11}{55} = \frac{264}{55} \]
Now simplifying \( \frac{264}{55} \):
\( 264 \div 11 = 24 \) and \( 55 \div 11 = 5 \)
So the equation becomes:
\[ 8(x + \frac{4}{5}) = \frac{24 \cdot 11}{5} = \frac{264}{55} \]
Dividing both sides by 8:
\[ x + \frac{4}{5} = \frac{264}{440} = \frac{3}{5} \]
Now solving for \( x \):
\[ x = \frac{3}{5} - \frac{4}{5} \]
Which simplifies to:
\[ x = -\frac{1}{5} \]
Thus, your solution \( x = \frac{13}{15} \) is incorrect. The correct solution is:
\[ x = -\frac{1}{5} \]