To solve the equation \( \frac{5}{3}x + \frac{11}{3} = -\frac{4}{3} \), we can follow your approach of isolating \( \frac{5}{3}x \).
- Start by subtracting \( \frac{11}{3} \) from both sides:
\[ \frac{5}{3}x = -\frac{4}{3} - \frac{11}{3} \]
- Combine the fractions on the right side:
\[ -\frac{4}{3} - \frac{11}{3} = -\frac{4 + 11}{3} = -\frac{15}{3} \]
- Simplifying \( -\frac{15}{3} \):
\[ -\frac{15}{3} = -5 \]
So now we have:
\[ \frac{5}{3}x = -5 \]
- To isolate \( x \), multiply both sides by the reciprocal of \( \frac{5}{3} \), which is \( \frac{3}{5} \):
\[ x = -5 \cdot \frac{3}{5} \]
- Simplifying gives:
\[ x = -3 \]
Thus, the solution is \( x = -3 \).
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