Expand -7/6 ( 3g + 2 )

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

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

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

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

Comparing this to your provided options, we see that the correct expansion is: \[ -\frac{7}{2}g - \frac{7}{3} \]

Summary of Options:

1. \(-\frac{7}{2}g - \frac{7}{3}\) (Correct)
2. \(\frac{7}{2}g - \frac{7}{3}\)
3. \(-\frac{7}{2}g + 2\)
4. \(\frac{7}{2}g + 2\)

Thus, the first option is the correct result after expanding the expression.