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Which expressions are equivalent to [tex]$3g + 6(-g + (-5))$[/tex]?

Choose all answers that apply:
A. [tex]$9g + 30$[/tex]
B. [tex][tex]$-3g - 30$[/tex][/tex]
C. None of the above


Sagot :

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