Question

Expand −7/6 ( 3 g + 2 )
.(1 point)
Responses

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

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

−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

Answer 1

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

1. Distributing to the first term:
\(-\frac{7}{6} \times 3g = -\frac{21}{6}g\)

2. Distributing to the second term:
\(-\frac{7}{6} \times 2 = -\frac{14}{6} = -\frac{7}{3}\)

Now, we can combine these results:

\[
-\frac{21}{6}g - \frac{7}{3}
\]

We can simplify \(-\frac{21}{6}g\) to \(-\frac{7}{2}g\) (by dividing both the numerator and the denominator by 3):

Thus, the final expanded expression is:

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

So the correct response is:

**negative Start Fraction 7 over 2 End Fraction g minus Start Fraction 7 over 3 End Fraction**