Question

using algebra tiles write the equation modeled by the algebra tiles. then solve the equation using algebra tiles. check your answer using properties of equality. (see exploration 1, p. 139.) 10. image of algebra tiles = image of algebra tiles 11. image of algebra tiles = image of algebra tiles

Explanation:

Problem 10:

Step1: Model the equation

Let green tiles be \( x \), yellow tiles be \( 1 \), red tiles be \( -1 \). Left side: \( 2x + 6(1) \), Right side: \( 4(-1) \). So equation: \( 2x + 6 = -4 \).

Step2: Solve with algebra tiles

Subtract 6 (yellow tiles) from both sides: \( 2x + 6 - 6 = -4 - 6 \) → \( 2x = -10 \). Divide both sides by 2: \( x = -5 \).

Step3: Check with properties

Start with \( 2x + 6 = -4 \). Subtraction property: \( 2x + 6 - 6 = -4 - 6 \) → \( 2x = -10 \). Division property: \( \frac{2x}{2} = \frac{-10}{2} \) → \( x = -5 \).

Step1: Model the equation

Let red tiles be \( -x \), yellow tiles be \( 1 \), red negative tiles be \( -1 \). Left side: \( 3(-x) + 4(1) \), Right side: \( 11(-1) \). Equation: \( -3x + 4 = -11 \).

Step2: Solve with algebra tiles

Subtract 4 (yellow tiles) from both sides: \( -3x + 4 - 4 = -11 - 4 \) → \( -3x = -15 \). Divide by -3: \( x = 5 \).

Step3: Check with properties

Start with \( -3x + 4 = -11 \). Subtraction property: \( -3x + 4 - 4 = -11 - 4 \) → \( -3x = -15 \). Division property: \( \frac{-3x}{-3} = \frac{-15}{-3} \) → \( x = 5 \).

Answer:

Equation: \( 2x + 6 = -4 \), Solution: \( x = -5 \)

Problem 11: