Question
Expand -7/6 ( 3g + 2 )
-7/2g - 7/3
7/2g - 7/3
-7/2g + 2
7/2g + 2
-7/2g - 7/3
7/2g - 7/3
-7/2g + 2
7/2g + 2
Answers
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Answered by
GPT-4o mini
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.
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.
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