Unit 2 Week 4 Reasoning with Linear Equations

Unit 2 – Week 4 Reasoning with Linear Equations and Inequalities Lesson 4 Students will apply the properties of equality to solve multi-step linear equations: starting from the assumption that the original equation has a solution. Students explain each step by following the properties of equality.

Standards • A. REI. 1 – Using algebraic properties and the properties of real numbers, justify the steps of a simple one-solution equation. • A. REI. 3 – Solve linear equations in one variable including equations with coefficients represented by letters.

Essential Questions • What are properties of equality? • How are the properties of equality used to solve equations?

Vocabulary Words • Properties of Equality: Rules that allow you to balance, manipulate and solve equations

Read, Write, Draw, Solve • Haley is working with the equation x + 4 = 3 x + 2. She wants to know that if she adds the expression x + 2 to both sides of the equation will this change the solution set. Show Haley is right or wrong in her thinking.

Activator • Solve the following equation and record your thinking as you perform each step. 5 x + 9 = 2 x – 36 What does your solution mean?

Complete the Table Equation 4 x – 15 = 17 – 4 x Steps Original Equation

Complete the Table Equation 3 x – 2 x = -4 x + 4 Steps Original Equation

Complete the Table Equation 4 t – 5 t + 9 = 5 t – 9 Steps Original Equation

Complete the Table Equation 53 a – 55 = 42 a Steps Original Equation

Complete the Table Equation 3(2 x – 4) = 6(x – 2) Steps Original Equation

Complete the Table Equation 8(3 x + 2) = 2(12 x – 5) Steps Original Equation

Complete the Table Equation 8 a – 15 – 6 a = 85 – 3 a Steps

Complete the Table Equation 3 m – 5 m – 12 = 73 – 88 – 50 Steps Original Equation

Complete the Table Equation 7 – 8 x = 7(1 + 7 x) Steps

Complete the Table Equation Steps

Summarizer Solve for x in the equation -5(-5 x – 6) = -22 – x Explain what this solution means.