Question

2.1.3 what does “minus” mean? writing algebraic expressions 2 - 25. building expressions use the expression mat to create each of the following expressions with algebra tiles. a. -3x + 4 b. -(y - 2) c. -y - 3 d. 5x-(3 - 2x)

Explanation:

Step1: Interpret -3x + 4

Use 3 negative \(x\) - tiles and 4 positive unit - tiles.

Step2: Simplify -(y - 2)

Apply the distributive property: \(-(y - 2)=-y + 2\). Use 1 negative \(y\) - tile and 2 positive unit - tiles.

Step3: Interpret -y - 3

Use 1 negative \(y\) - tile and 3 negative unit - tiles.

Step4: Simplify 5x-(3 - 2x)

First, distribute the negative sign: \(5x-(3 - 2x)=5x-3 + 2x\). Then combine like - terms: \(5x+2x-3 = 7x-3\). Use 7 positive \(x\) - tiles and 3 negative unit - tiles.

Answer:

a. 3 negative \(x\) - tiles and 4 positive unit - tiles; b. 1 negative \(y\) - tile and 2 positive unit - tiles; c. 1 negative \(y\) - tile and 3 negative unit - tiles; d. 7 positive \(x\) - tiles and 3 negative unit - tiles.