Linear Expressions & Single-Variable Equations/Inequalities

Lesson 4

Math

Unit 3

9th Grade

Lesson 4 of 12

Objective


Solve equations with a variable in the denominator.

Common Core Standards


Core Standards

  • F.IF.A.1 — Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
  • 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
  • 8.F.A.1

Criteria for Success


  1. Describe that dividing by zero produces an expression that is undefined. 
  2. Describe that when a variable is the divisor, there is a “domain restriction” on possible values for the variable so the expression is defined. 
  3. Identify the domain restriction when there is a variable in the denominator. 
  4. Identify equations with no solutions, based on a domain restriction of one side of the equation. 
  5. Efficiently solve an equation with a variable in the denominator.

Tips for Teachers


A common misconception can arise from students treating terms in the numerator or denominator separately instead of as grouped expressions when operating. Ensure students use parentheses around expressions in the numerator or denominator of an expression when solving to minimize this misconception.

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Anchor Problems

25-30 minutes


Problem 1

Solve for $$x$$, if possible. 

a.    $$\frac{x}{4}=5$$

 

b.    $$\frac{x}{\frac{1}{2}}=6$$

 

c.    $$\frac{x}{0}=10$$

Guiding Questions

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Problem 2

Solve both of the equations below.

 

$${10=\frac{x-2}{5}}$$

 

$${10=\frac{5}{x-2}}$$, where $${x\neq2}$$

Guiding Questions

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Problem 3

Identify any domain restrictions and solve the equation below. 

$${\frac{3}{x}=\frac{2}{x+2}}$$

Guiding Questions

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Problem Set

15-20 minutes


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

Target Task

5-10 minutes


Problem 1

Solve for $$x$$.

$$\frac{x-2}{x-9}=2$$

References

EngageNY Mathematics Algebra I > Module 1 > Topic C > Lesson 18Exit Ticket

Algebra I > Module 1 > Topic C > Lesson 18 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by Fishtank Learning, Inc.

Problem 2

Write an equation that would have the restriction $${x\neq-3}$$.

References

EngageNY Mathematics Algebra I > Module 1 > Topic C > Lesson 18Exit Ticket

Algebra I > Module 1 > Topic C > Lesson 18 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

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.

  • Include problems where students need to identify domain restrictions in an expression but not solve an equation.
  • Include problems where the domain restriction is the only solution to the equation. Ensure students are identifying that the solution is undefined.

Next

Solve for a variable in an equation or formula.

Lesson 5
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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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