To determine which expressions are equivalent to [tex]\(3g + 6(-g + (-5))\)[/tex], let's simplify the expression step-by-step:
1. Start with the given expression:
[tex]\[
3g + 6(-g + (-5))
\][/tex]
2. Simplify inside the parentheses first:
[tex]\[
-g + (-5) = -g - 5
\][/tex]
3. Substitute this back into the expression:
[tex]\[
3g + 6(-g - 5)
\][/tex]
4. Distribute the 6 through the parentheses:
[tex]\[
3g + 6(-g) + 6(-5)
\][/tex]
5. Perform the multiplication:
[tex]\[
3g + (-6g) + (-30)
\][/tex]
[tex]\[
3g - 6g - 30
\][/tex]
6. Combine like terms:
[tex]\[
(3g - 6g) - 30 = -3g - 30
\][/tex]
After simplifying, the expression [tex]\(3g + 6(-g + (-5))\)[/tex] simplifies to [tex]\(-3g - 30\)[/tex].
Now we compare this simplified result to the given choices:
- [tex]\(9g + 30\)[/tex]:
[tex]\[
-3g - 30 \quad \text{is not equal to} \quad 9g + 30
\][/tex]
- [tex]\(-3g - 5\)[/tex]:
[tex]\[
-3g - 30 \quad \text{is not equal to} \quad -3g - 5
\][/tex]
- None of the above:
Since neither [tex]\(9g + 30\)[/tex] nor [tex]\(-3g - 5\)[/tex] are equivalent to [tex]\(-3g - 30\)[/tex]:
The correct answer is [tex]\(None of the above\)[/tex].
Hence, the answer is:
c. None of the above
