Expand −7/6(3g+2)

.(1 point)
Responses

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

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

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

72g+2

1 answer

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

  1. Distributing to the first term: \[ -\frac{7}{6} \cdot 3g = -\frac{7 \cdot 3}{6}g = -\frac{21}{6}g = -\frac{7}{2}g \] (since \(21\) divided by \(3\) is \(7\), and \(6\) divided by \(3\) is \(2\)).

  2. Distributing to the second term: \[ -\frac{7}{6} \cdot 2 = -\frac{7 \cdot 2}{6} = -\frac{14}{6} = -\frac{7}{3} \] (since \(14\) divided by \(2\) is \(7\), and \(6\) divided by \(2\) is \(3\)).

Combining both results, we get: \[ -\frac{7}{2}g - \frac{7}{3} \]

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

This matches the response option: "− Start Fraction 7 over 2 End Fraction g minus Start Fraction 7 over 3 End Fraction".