To solve the equation \( \frac{5}{3}x + \frac{11}{3} = -\frac{4}{3} \), follow these steps:
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Isolate the term with \( x \) by subtracting \( \frac{11}{3} \) from both sides:
\[ \frac{5}{3}x = -\frac{4}{3} - \frac{11}{3} \]
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Combine the fractions on the right side:
\[ -\frac{4}{3} - \frac{11}{3} = -\frac{4 + 11}{3} = -\frac{15}{3} = -5 \]
So we have:
\[ \frac{5}{3}x = -5 \]
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Solve for \( x \) by multiplying both sides of the equation by the reciprocal of \( \frac{5}{3} \), which is \( \frac{3}{5} \):
\[ x = -5 \times \frac{3}{5} \]
\[ x = -\frac{15}{5} = -3 \]
So, the solution is:
\[ \boxed{-3} \]