Question

Which expressions are equivalent to 6 + 12x?

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Answer 1

Expressions A, C, D are equivalent

Explanation:

Equivalent expressions:

Two expressions are equivalent if they give the same result. So

Option A:

3(2 + 4x) =3*2 + 3*4x = 6 + 12x

So equivalent

Option B:

3(2 + 6x) + 2x = 3*2 + 3*6x + 2x = 6 + 18x + 2x = 6x + 20. So not equivalent

Option C:

5(1+2x) + 1 + 2x = 5*1 + 5*2x + 1 + 2x = 5 + 10x + 1 + 2x = 6 + 12x.

Equal, so equivalent

Option D:

7*(1+2x) - 2x - 1 = 7*1 + 7*2x - 2x - 1 = 7 + 14x - 2x - 1 = 6 + 12x

Equal, so equivalent.

Option E:

7*(1+2x) + 2x - 1 = 7*1 + 7*2x - 2x - 1 = 7 + 14x + 2x - 1 = 6 + 16x

Different, so not equivalent.