Question

Cheri and Sharon are finding equivalent expressions for the expression below.

6(x + 2) + 2(3x + 2x) + 20

* Cheri claims the expression is equivalent to 16x + 32.
* Sharon says that this expression is equivalent to 48x.
Part A

Which girl’s expression is equivalent to the original expression? Support your answer by showing how the original expression can be rewritten as an equivalent expression with the fewest terms. (2 pts.)

Part B

Which girl’s expression is not equivalent to the original expression? Support your answer by identifying the mistake(s) made when rewriting the original expression as an equivalent expression with the fewest terms. (2 pts.)

Answer 1

Explanation:

6(x + 2) + 2(3x + 2x) + 20

6x + 12 + 2×5x + 20

6x + 12 + 10x + 20

16x + 32

so, Cheri is right.

it seems like Sharon thought that all terms in the expression contain "x", and so she could add all constant factors into one term for x.

which gave her 16+32 = 48x

but because "2" and "20" are constants without any associated variable, they cannot be combined and simplified with terms that contain a variable (or a different variable : e.g. if there were terms for x and other terms for y, they cannot be combined either).

only terms with the same form of variable(s) can be combined and simplified. otherwise they need to start apart.

Answer 2

Answer: Cheri is correct; the expression is simplified to 16x + 32

Explanation:

6(x + 2) + 2(3x + 2x) + 20

6x+ 12 + 6x + 4x + 20

combine like terms:

16x + 32

Mistakes Sharon made:

- added 16x + 32 (not like terms)