Expand −7/6(3g+2).(1 point)

Question

Responses

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

7/2g−7/3
Start Fraction 7 over 2 End Fraction g minus Start Fraction 7 over 3 End Fraction

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

−7/2g−7/3

Answer 1

To expand the expression \(-\frac{7}{6}(3g + 2)\), we distribute \(-\frac{7}{6}\) to both terms inside the parentheses:

\[ -\frac{7}{6} \cdot 3g - \frac{7}{6} \cdot 2 \]

Calculating each term:

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

2. For the second term: \[ -\frac{7 \cdot 2}{6} = -\frac{14}{6} = -\frac{7}{3} \quad (\text{since } \frac{14}{6} = \frac{7}{3}) \]

Putting it all together, we get:

\[ -\frac{7}{2}g - \frac{7}{3} \]

Thus, the fully expanded expression is:

\[ -\frac{7}{2}g - \frac{7}{3} \]

The correct response from your options is: \[ −\frac{7}{2}g−\frac{7}{3} \]