The Distributive Property & Algebraic Expressions Quick Check

Question

Expand —7/6 (3g + 2).
A: —7/2g + 2
B: 7/2g + 2
C: —7/2g — 7/3
D: 7/2g — 7/3

Answer 1

To expand the expression \(-\frac{7}{6}(3g + 2)\), we will use the distributive property, which states that \(a(b + c) = ab + ac\).

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

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

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

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

The correct answer is: C: \(-\frac{7}{2}g - \frac{7}{3}\).