Let's solve the equation step-by-step and fill in the blanks:
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Start with the original equation: \[ \frac{5}{3}x + \frac{11}{3} = -\frac{4}{3} \]
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Subtract \(\frac{11}{3}\) from both sides: \[ \frac{5}{3}x = -\frac{4}{3} - \frac{11}{3} \] Combine the fractions on the right side: \[ -\frac{4 + 11}{3} = -\frac{15}{3} = -5 \] Thus, we have: \[ \frac{5}{3}x = -5 \]
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Now we need to multiply both sides by \(\frac{3}{5}\), the reciprocal of \(\frac{5}{3}\): \[ x = -5 \cdot \frac{3}{5} \]
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Simplifying the right side: \[ x = -3 \]
Now, we can fill in the blanks:
- In the first blank for \(\frac{5}{3}x =\), you fill in −5.
- In the second blank for \(x =\), you fill in −3.
- For the final operation, you multiply both sides by \(\frac{3}{5}\).
So, the completed solution is: \[ 5/3x = -5 \] \[ x = -3 \] Multiply both sides by \(\frac{3}{5}\).