Question

Which expressions are equivalent to −3(2w+6)−4?

A = 6w−14
B = 2(−3w+(−11))
C = None of the above

Answer 1

The equivalent expression to −3(2w+6)−4, after using the distributive property and combining like terms, is 2(−3w+(−11)). This corresponds to Option B in the choices provided.

Step-by-step explanation:

The question asks which expressions are equivalent to the expression −3(2w+6)−4. To find the equivalent expressions, we need to use the distributive property and combine like terms.

First, apply the distributive property: −3 × 2w gives us −6w, and −3 × 6 gives us −18. So the expression becomes −6w −18 −4.

Next, combine like terms by adding the constants: −18 and −4 gives us −22. So the expression simplifies to −6w −22.

Now let's compare this with the given options:

• Option A: 6w−14 is not equivalent because the coefficient of w is positive in Option A, but negative in the simplified expression.
• Option B: 2(−3w+(−11)) simplifies to −6w−22, which is equivalent to our simplified expression.
• Option C: None of the above is incorrect because we found that Option B is equivalent.

Therefore, the equivalent expression to −3(2w+6)−4 is Option B: 2(−3w+(−11)).