To solve the equation \( \frac{5}{3}x - 4 = -9 \), follow these steps:
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Add 4 to both sides to isolate the term with \( x \): \[ \frac{5}{3}x - 4 + 4 = -9 + 4 \] Simplifying gives: \[ \frac{5}{3}x = -5 \]
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Multiply both sides by the reciprocal of \( \frac{5}{3} \), which is \( \frac{3}{5} \): \[ x = -5 \cdot \frac{3}{5} \] This simplifies to: \[ x = -3 \]
Thus, the solution is: \[ \boxed{-3} \]