Question

Heather says that the expressions 4 x minus 2 x plus 8 and 2 left parenthesis x plus 4 right parenthesis are not equivalent because one expression has a term that is subtracted and the other does not. Do you​ agree? Explain.

Answer 1

Yes, Heather is correct. The expressions are not equivalent

Solution:

Given that,

Heather says, the following expressions are not equivalent

$4x - 2x + 8\ and\ 2(x-4)$

Because one expression has a term that is subtracted and the other does not

Combine the like terms in first expression:

$4x - 2x + 8 = 2x +8$

Let us first expand the second expression

By distributive property

a(b + c) = ab + bc

Therefore,

$2(x-4) = 2x - 8$

Thus the two expressions are:

$2x + 8\ and\ 2x-8$

Yes both the expressions are not equivalent

Because, in first expression 2x is added to 8

But in second expression, 8 is subtracted from 2x

Thus heather is correct