Question

answer the parts below
(a) choose the correct way to show $2 + 7x$ using algebra tiles.
(b) choose the correct way to show $7x + 2$ using algebra tiles.
(c) are $2 + 7x$ and $7x + 2$ equivalent?
○yes
○no

Explanation:

Step1: Analyze 2 + 7x with tiles

Algebra tiles: $x$ = green rectangle, constant = blue square. $2+7x$ needs 2 blue squares + 7 green rectangles. The second tile set matches this: 2 green $x$ tiles? No, correction: 7 blue $x$? Wait, no: the second option in (a) has 7 blue rectangles (for $7x$) and 2 green squares (constants). That is $2 + 7x$.

Step2: Analyze 7x + 2 with tiles

$7x+2$ is same tile count: 7 $x$-tiles + 2 constants. The second tile set in (b) also matches (7 blue $x$-tiles + 2 green constants), same as (a) just ordered same, which is valid.

Step3: Check equivalence

Addition is commutative: $a+b = b+a$, so $2+7x=7x+2$.

Answer:

(a) The second tile set (7 blue rectangular tiles + 2 green square tiles)
(b) The second tile set (7 blue rectangular tiles + 2 green square tiles)
(c) Yes