Expand −7/6(3g+2)

Question

.(1 point)
Responses

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

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

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

−7/2g−7/3

Answer 1

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

1. Multiply \(-\frac{7}{6}\) by \(3g\): \[ -\frac{7}{6} \cdot 3g = -\frac{7 \cdot 3}{6}g = -\frac{21}{6}g = -\frac{7}{2}g \]

2. Multiply \(-\frac{7}{6}\) by \(2\): \[ -\frac{7}{6} \cdot 2 = -\frac{14}{6} = -\frac{7}{3} \]

Now, combine the results: \[ -\frac{7}{2}g - \frac{7}{3} \]

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

Thus, the correct response is: −7/2g−7/3