Question

Show your work.
Are the expressions (4c + 8) + 3c - 2 and 4c + 2(0.5c + 1) equivalent?

Answer 1

First, let's simplify the expression (4c + 8) + 3c - 2:

(4c + 8) + 3c - 2

= 4c + 3c + 8 - 2 (rearrange terms)

= 7c + 6 (combine like terms)

So the first expression simplifies to 7c + 6.

Next, let's simplify the expression 4c + 2(0.5c + 1):

4c + 2(0.5c + 1)

= 4c + 2(0.5c) + 2(1) (distribute the 2)

= 4c + c + 2 (simplify the parenthesis)

= 5c + 2 (combine like terms)

So the second expression simplifies to 5c + 2.

Now we can compare the two expressions:

7c + 6 vs. 5c + 2

These expressions are not equivalent because they do not have the same coefficients or constants.