Question

eloises math tutor used algebra tiles to model $3n + 4 - n + 5$. what is the simplified form of this expression?

1. eloise rearranged the tiles as shown below. what property did she use? write an expression that represents eloises arrangement of the tiles.

1. rewrite your expression from exercise 1 by grouping like terms.

1. what is the simplified form of the expression?

Explanation:

Step1: Identify property for rearrangement

Eloise used the Commutative Property of Addition (this allows reordering terms without changing the sum). Count the tiles: 3 positive $n$-tiles, 1 negative $n$-tile, and $4+5=9$ constant tiles. The rearranged expression is $3n - n + 4 + 5$.

Step2: Group like terms

Group the variable terms and constant terms together:
$(3n - n) + (4 + 5)$

Step3: Combine like terms

Calculate the variable terms: $3n - n = 2n$
Calculate the constant terms: $4 + 5 = 9$

Step4: Simplify the original expression

Combine the results from Step3: $2n + 9$

Answer:

1. Property: Commutative Property of Addition; Rearranged expression: $3n - n + 4 + 5$
2. Grouped expression: $(3n - n) + (4 + 5)$
3. Simplified form: $2n + 9$