Expand −7/6(3g+2)

.(1 point)
Responses

−72g−73
negative Start Fraction 7 over 2 End Fraction g minus Start Fraction 7 over 3 End Fraction

−72g+2
negative Start Fraction 7 over 2 End Fraction g plus 2

72g+2
Start Fraction 7 over 2 End Fraction g plus 2

72g−73

1 answer

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:

  1. For \(-\frac{7}{6}(3g)\): \[ -\frac{7 \cdot 3g}{6} = -\frac{21g}{6} = -\frac{7g}{2} \quad \text{(simplifying \(-\frac{21}{6}\))} \]

  2. 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.