Which expressions are equivalent to
\[-3(2w+6)-4\] ?
Choose all answers that apply:
Choose all answers that apply:
(Choice A)
\[6w-14\]
A
\[6w-14\]
(Choice B)
\[2(-3w+(-11))\]
B
\[2(-3w+(-11))\]
(Choice C) None of the above
C
None of the above
To simplify the expression \(-3(2w+6)-4\), we can apply the distributive property:
\[-3(2w+6)-4 = -6w-18-4.\]
Simplifying further, we combine like terms:
\[-6w-18-4 = -6w-22.\]
Therefore, none of the given choices (\(6w-14\) and \(2(-3w+(-11))\)) are equivalent expressions to \(-3(2w+6)-4\).
The correct choice is C: None of the above.
To find the equivalent expressions, let's simplify \(-3(2w+6)-4\) step by step.
Step 1: Distribute the -3 to the terms inside the parentheses.
\(-3(2w+6) = -6w - 18\)
Step 2: Subtract 4 from the result.
\(-6w - 18 - 4 = -6w - 22\)
Now let's compare this expression to the given choices:
Choice A: \(6w-14\) - This expression is not equivalent to the given expression.
Choice B: \(2(-3w+(-11))\) - To simplify this, first distribute the 2 to the terms inside the parentheses.
\(2(-3w+(-11)) = -6w - 22\)
This expression is equivalent to the given expression.
Since Choice B matches the simplified form step-by-step, the correct answer is:
Choice B: \(2(-3w+(-11))\)
Therefore, the answer is only Choice B.
To find the equivalent expressions, we need to simplify the given expression \[-3(2w+6)-4\].
Step 1: Distribute the -3 to the terms inside the parentheses:
\[-3 \times 2w = -6w\]
\[-3 \times 6 = -18\]
The expression becomes:
\[-6w - 18 - 4\]
Step 2: Combine like terms:
\[-6w - 18 - 4 = -6w - 22\]
Now, let's compare the simplified expression \[-6w - 22\] with the given options:
Choice A: \[6w-14\]
This expression is different from the simplified expression, so it is not equivalent.
Choice B: \[2(-3w+(-11))\]
To simplify this expression, we distribute 2 to the terms inside the parentheses:
\[2 \times -3w = -6w\]
\[2 \times -11 = -22\]
The expression becomes:
\[-6w - 22\]
This expression matches the simplified expression, so it is equivalent.
Now, we have determined that Choice B (\[2(-3w+(-11))\]) is equivalent to the given expression.
Therefore, the answer is:
- Choice A: None
- Choice B: Equivalent
- Choice C: None
So, the correct choice is B.