To expand the expression \(-\frac{7}{6}(3g + 2)\), you apply the distributive property:
\[ -\frac{7}{6}(3g) - \frac{7}{6}(2) \]
Now, calculate each term:
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For \(-\frac{7}{6}(3g)\): \[ -\frac{7 \cdot 3g}{6} = -\frac{21g}{6} = -\frac{7g}{2} \quad \text{(simplifying \(-\frac{21}{6}\))} \]
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For \(-\frac{7}{6}(2)\): \[ -\frac{7 \cdot 2}{6} = -\frac{14}{6} = -\frac{7}{3} \quad \text{(simplifying \(-\frac{14}{6}\))} \]
Now combine the results:
\[ -\frac{7}{2}g - \frac{7}{3} \]
The expanded expression is:
\[ -\frac{7}{2}g - \frac{7}{3} \]
Thus, the correct response from the options provided is:
negative Start Fraction 7 over 2 End Fraction g minus Start Fraction 7 over 3 End Fraction.