To solve the equation
\[ \frac{5}{3}x + \frac{11}{3} = -\frac{4}{3} \]
we can follow these steps:
- Subtract \(\frac{11}{3}\) from both sides:
\[ \frac{5}{3}x = -\frac{4}{3} - \frac{11}{3} \]
- Combine the fractions on the right side:
\[ -\frac{4}{3} - \frac{11}{3} = -\frac{4 + 11}{3} = -\frac{15}{3} \]
So we have:
\[ \frac{5}{3}x = -\frac{15}{3} \]
- Simplify the right side:
\[ -\frac{15}{3} = -5 \]
Now the equation becomes:
\[ \frac{5}{3}x = -5 \]
- Now, multiply both sides by \(\frac{3}{5}\) to solve for \(x\):
\[ x = -5 \cdot \frac{3}{5} \]
- Calculate \(x\):
\[ x = -\frac{15}{5} = -3 \]
Thus, the solution to the equation is:
\[ x = -3 \]