Linear Expressions & Single-Variable Equations/Inequalities

Lesson 3

Math

Unit 3

9th Grade

Lesson 3 of 12

Objective


Solve single-variable linear equations using properties of equality.

Common Core Standards


Core Standards

  • A.REI.A.1 — Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
  • A.REI.B.3 — Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

Foundational Standards

  • 8.EE.C.7.B

Criteria for Success


  1. Use additive and multiplicative identity properties to solve an equation. 
  2. Identify efficient methods to solve a linear equation using properties of equality. 
  3. Describe that each step in solving an equation creates an equation that is equivalent to the rest of the equations created. 
  4. Identify the reason(s) for each step in solving an equation. 
  5. Check solutions by substituting calculated values in the equation. Describe how you know your solution makes sense.

Tips for Teachers


A misconception students may continue to have is incorrectly operating with fraction coefficients and constants while solving an equation.

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Anchor Problems


Problem 1

Solve the following equation.


$${3x-[8-3(x-1)] = x + 19}$$

Guiding Questions

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Problem 2

Solve the following equation: 

$${\frac{1}{2} (x-6)-2(3-2x)=6-2(4x+1)}$$

Guiding Questions

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Problem Set


Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task


Solve the equations for $$x$$. For each step, describe the properties of operations and/or the properties of equality used to transform and solve the equation. 

a.     $$5(2x-4)-11=4+3x$$

 

b.     $$\frac{1}{4}(8x+3)-5=x-5$$

 

c.     $$3-\frac{1}{2} x-8(3x-2)=10$$

 

d.     $$3x+2-4(2x+3)=12$$

Additional Practice


The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

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Lesson 2

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Lesson 4

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Properties and Solutions of Single-Variable Linear Expressions and Equations

Topic B: Modeling with Single-Variable Linear Equations

Topic C: Properties and Solutions of Single-Variable Linear Inequalities

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