Unit 2 – Week 4Reasoning 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 = 3x + 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 how Haley is right or wrong in her thinking.

Activator

• Solve the following equation and record your thinking as you perform each step.

5x + 9 = 2x – 36

What does your solution mean?

Complete the Table

Equation Steps

4x – 15 = 17 – 4x Original Equation

Complete the Table

Equation Steps

3x – 2x = -4x + 4Original Equation

Complete the Table

Equation Steps

4t – 5t + 9 = 5t – 9 Original Equation

Complete the Table

Equation Steps

53a – 55 = 42a Original Equation

Complete the Table

Equation Steps

3(2x – 4) = 6(x – 2) Original Equation

Complete the Table

Equation Steps

8(3x + 2) = 2(12x – 5) Original Equation

Complete the Table

Equation Steps

8a – 15 – 6a = 85 – 3a

Complete the Table

Equation Steps

3m – 5m – 12 = 73 – 88 – 50 Original Equation

Complete the Table

Equation Steps

7 – 8x = 7(1 + 7x)

Complete the Table

Equation Steps

Summarizer

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