To solve the equation \( \frac{5}{3}x + \frac{11}{3} = -\frac{4}{3} \), we'll first isolate \( x \).
- Subtract \( \frac{11}{3} \) from both sides:
\[ \frac{5}{3}x = -\frac{4}{3} - \frac{11}{3} \]
- Combine the fractions on the right side:
\[ -\frac{4}{3} - \frac{11}{3} = -\frac{4 + 11}{3} = -\frac{15}{3} = -5 \]
So, we have:
\[ \frac{5}{3}x = -5 \]
- Now, multiply both sides by the reciprocal of \( \frac{5}{3} \) (which is \( \frac{3}{5} \)) to solve for \( x \):
\[ x = -5 \times \frac{3}{5} = -3 \]
Thus, \( x = -3 \).
Next, we calculate what \( \frac{5}{3}x \) equals when \( x = -3 \):
\[ \frac{5}{3}x = \frac{5}{3} \times -3 = -5 \]
So, the answers are:
- \( x = -3 \)
- \( \frac{5}{3}x = -5 \)