Solving Multistep Linear Equations Using Algebra Tiles

Objectives Solving Equations Involving the Distributive Property Solving Multi-Step Equations

The development of the equation solving model is based on two ideas. Solving Equations The development of the equation solving model is based on two ideas. Variables can be isolated by using zero pairs. Equations are unchanged if equivalent amounts are added to each side of the equation.

Solving an Equation Using the Distributive Property Solve: 2(x - 2) = 6 How can we model this equation? Hint: form two groups of x – 2. What can we do to isolate the x-tiles? We want to get x alone for a solution, but first we need to make two groups of equal tiles on each side of the bar. What is the result? 2(x - 2) = 6 2x – 4 = 6 +4 + 4 2x = 10 2 2 x = 5 = X = 5

Solving an Equation Using the Distributive Property Solve: -4(x + 2) = 8 How can we model this equation? What can we do to isolate the x-tiles? We want to get x alone for a solution, but first we need to make four groups of equal tiles on each side of the bar. What is the result? -4(x + 2) = 8 -4x - 8 = 8 +8 +8 -4x = 16 -4 -4 x = -4 = X = -4

Solving a Multi-Step Equation 5x + 2 = 3x + 8 -3x -3x 2x + 2 = 8 -2 -2 2x = 6 2 2 x = 3 Solve: 5x + 2 = 3x + 8 How can we model this equation? We need to combine variables and constants separately? We want to get x alone for a solution, but first we need to make two groups of equal tiles on each side of the bar. What is the result? = X = 3

Practice Solving Linear Equations Algebraically (without using Algebra Tiles) Solve: 5(x - 3) = 10 Solve: 2( x – 3) = 6 Solve: 4x – 7 = 2x + 3 Solve: 7y + 2 = 6 + 2y Solve: 8(q + 9) = 6(2 – 2q) Solve: 10(10 + r) = 5(3r – 12)