Patterns, Functions, and Algebra
Focus: Linear Relationships
The student will
b) solve twostep linear inequalities and graph the results on a number line.



Essential Knowledge and Skills 
 Solve twostep inequalities in one variable by showing the steps and using algebraic sentences.
 Graph solutions to twostep linear inequalities on a number line.

Essential Understandings 
 How does the solution to an equation differ from the solution to an inequality? While a linear equation has only one replacement value for the variable that makes the equation true, an inequality can have more than one.


Vertical Articulation 
 SOL 6.18  solve onestep linear equations in one
variable
 SOL 7.14ab  a) solve one and twostep linear
equations; b) solve practical problems in one
variable
 SOL A.2  perform operations on polynomials  a)
apply laws of exponents to perform ops on
expressions; b) add/subtract/multiply/divide polynomials; c) factor first and second
degree binomials/trinomials (1 or 2
variables)
 SOL A.4  solve multistep linear/quad equation (in
2 variables)  a) solve leteral equation; b)
justify steps used in simplifying expressions
and solving equations; c) solve quad
equations (algebraically/graphically); d) solve
multistep linear equations
(algebraically/graphically); e) solve systems
of two linear equation (2 variable algebraically/graphically); f) solve realworld
problems involving equations and systems of
equations

Instructional Materials 
 VDOE Enhanced Scope and Sequence Lesson: Solving and Graphing Inequalities (PDF)  Solving and graphing inequalities (Word)
 Notes: Inequalities (flipchart)
 Activity: Solving Inequalities (doc)
 Activity: Solving Inequalities Matching (doc)

Real World Lessons 

Practice 
 Worksheet: Inequalities Practice (doc)
 Worksheet: Equations and Inequalities Review (doc)
 Worksheet: MultiStep Inequalities Word Problems (doc)
 Worksheet: Solving Inequalities Web Recording Sheet (doc)

SelfAssessments 
 SOL 8.15 MiniQuiz: Equations, Inequalities, and Properties

Skills 

Videos 
 PH Solving TwoStep Inequalities

Explore
Learning 
 Solving Linear Inequalities using Addition and Subtraction: Solve a linear inequality. Graph the solution on a dynamic number line.
 Solving Linear Inequalities using Multiplication and Division: Solve an inequality involving multiplication and division. Graph the solution on a number line.
 Compound Inequalities: Explore the graphs of two inequalities and find their union or intersection. Determine the relationship between the endpoints of the inequalities and the endpoints of the compound inequality.

Websites 
 Interactive Notes: Solving Inequalities  lessons and practice problems at Regentsprep.org
 Interactive Notes: Solving two step inequalities  notes and workout problems from Math.com

VDOE Interventions 
 VDOE Algebra Readiness Curriculum Companion: Using Order of Operations and Exploring Properties  (SOL 8.15c) The lessons focus on order of operations and evaluating numerical expressions. Students
will also investigate and recognize properties of real numbers used to solve an equation. (pdf)
 VDOE Algebra Readiness Curriculum Companion: Investigating Patterns, Functions, and Algebra  The lessons focus on algebraic reasoning. Students learn to solve equations and inequalities, first by using manipulatives and then by working with
symbols. They use modeling to collect data, and they learn to record data so that they can see the
relationship that exists among tables, graphs, words, and equations. (pdf)

Common Core
Standards 
7.EE.1 
7.EE.4a 
7.EE.4b 
8.EE.7a 
8.EE.7b 
