Let's go through the given expression and simplify it step by step.
The original expression is:
[tex]\[ -3(2w + 6) - 4 \][/tex]
Step-by-Step Solution:
1. Distribute -3 inside the parenthesis:
[tex]\[ -3(2w + 6) = -3 \cdot 2w + (-3) \cdot 6 \][/tex]
Simplifying this, we get:
[tex]\[ -3 \cdot 2w = -6w \][/tex]
[tex]\[ -3 \cdot 6 = -18 \][/tex]
So now the expression is:
[tex]\[ -6w - 18 - 4 \][/tex]
2. Combine like terms:
Combine the constants (-18 and -4):
[tex]\[ -6w - 18 - 4 = -6w - 22 \][/tex]
Now we will check each of the given options to see if any match our simplified expression [tex]\(-6w - 22\)[/tex].
- Option (A): [tex]\(6w - 14\)[/tex]
Clearly, [tex]\(6w - 14\)[/tex] is not equal to [tex]\(-6w - 22\)[/tex]. So, this option is incorrect.
- Option (B): [tex]\(2(-3w \div (-11))\)[/tex]
First, simplify inside the parenthesis:
[tex]\[ -3w \div (-11) = \frac{3w}{11} \][/tex]
Now, multiply by 2:
[tex]\[ 2 \left(\frac{3w}{11}\right) = \frac{6w}{11} \][/tex]
This result is [tex]\(\frac{6w}{11}\)[/tex], which is clearly not equal to [tex]\(-6w - 22\)[/tex]. So, this option is incorrect.
Given our analysis, none of the given options (A or B) are equivalent to [tex]\(-6w - 22\)[/tex].
- Option (C): None of the above
Given that neither option (A) nor option (B) matches [tex]\(-6w - 22\)[/tex], option (C) correctly reflects this.
Thus, the correct answer is:
[tex]\[ \boxed{\text{None of the above}} \][/tex]
