Let's solve the equation step by step. We start with:
\[ \frac{5}{3}x + \frac{11}{3} = -\frac{4}{3} \]
Step 1: Isolate \( \frac{5}{3}x \)
Subtract \( \frac{11}{3} \) from both sides:
\[ \frac{5}{3}x = -\frac{4}{3} - \frac{11}{3} \]
Step 2: Combine the fractions on the right side
To subtract the fractions, combine them over a common denominator:
\[ -\frac{4}{3} - \frac{11}{3} = -\frac{4 + 11}{3} = -\frac{15}{3} \]
Step 3: Simplify the fraction
\(-\frac{15}{3}\) can be simplified to:
\[ -\frac{15}{3} = -5 \]
So now we have:
\[ \frac{5}{3}x = -5 \]
Step 4: Solve for \(x\)
Now, to isolate \(x\), multiply both sides by the reciprocal of \( \frac{5}{3} \), which is \( \frac{3}{5} \):
\[ x = -5 \cdot \frac{3}{5} \]
Step 5: Simplify
Calculating the right side, we get:
\[ x = -\frac{15}{5} = -3 \]
Summary of results:
- \( \frac{5}{3}x = -5 \)
- \( x = -3 \)
Thus, the answers are:
\[ \frac{5}{3}x = -5 \]
and
\[ x = -3 \]