Question

Expand −7/6(3g+2) .(1 point) Responses 7/2g−7/3 Start Fraction 7 over 2 End Fraction g minus Start Fraction 7 over 3 End Fraction −7/2g−7/3 negative Start Fraction 7 over 2 End Fraction g minus Start Fraction 7 over 3 End Fraction 7/2g+2 Start Fraction 7 over 2 End Fraction g plus 2 −7/2g+2

Answer 1

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

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

2. **Distributing to the second term**:
\[
-\frac{7}{6} \cdot 2 = -\frac{14}{6} = -\frac{7}{3} \quad (\text{simplifying } -\frac{14}{6})
\]

Now, putting it all together, we have:
\[
-\frac{7}{6}(3g + 2) = -\frac{7}{2}g - \frac{7}{3}
\]

So the final expanded expression is:
\[
-\frac{7}{2}g - \frac{7}{3}
\]

The correct answer from the options provided is:
**\(-\frac{7}{2}g - \frac{7}{3}\)**.