A.5cd 
The student will solve multistep linear inequalities in two variables, including
c) solving realworld problems involving inequalities; and
d) solving systems of inequalities. 

Essential Knowledge and Skills 
 Solve realworld problems involving inequalities.
 Solve systems of linear inequalities algebraically and graphically.

Essential Understandings 
 A solution to an inequality is the value or set of values that can be substituted to make the inequality true.
 Realworld problems can be modeled and solved using linear inequalities.
 Set builder notation may be used to represent solution sets of inequalities.


Vertical Articulation 
 SOL 7.15  a) solve onestep inequalities; b) graph solutions on number line
 SOL 8.15  b) solve twostep linear inequalities and graph results on number line; c) ID properties of operations used to solve
 SOL AFDA.5  determine opt values in problem situations by identifying constraints/using linear programming techniques
 SOL AII.5  solve nonlinear systems (algebraically/ graphically)

Instructional Materials 
 VDOE ESS Lesson: Graphing Systems of Inequalities  Equations and Inequalities (PDF)  Graphing systems of inequalities (Word)
 Notes: Graphing Systems of Inequalities (ppt)

Real World Lessons 

Practice 
 VDOE ESS: Solving Inequalities in One and Two Variables Worksheet (pdf)
 VDOE ESS: Graphing Systems of Inequalities Worksheet (pdf)  Answer Key (pdf)
 VDOE ESS: What Can I Buy Worksheet (pdf)
 Worksheet: Solving Systems of Inequalities CW (doc)
 Worksheet: Solving Systems of Inequalities HW (doc)
 ExamView Quiz: Solving Systems of Inequalities by Graphing
 ExamView: Systems of Inequalities Quiz
 Prentice Hall Quiz  Systems of Inequalities

SelfAssessments 

Skills 
 JMU Pivotal Question: System of Inequalities Graph (doc)
 JMU Pivotal Question: System of Inequalities Graph #2 (doc)

Videos 
 Video: PH Graphing Systems of Linear Inequalities
 Video: PH Writing Systems of Linear Inequalities
 Video: PH Using a System of Linear Inequalities
 Video Tutor  Solving a System of Linear Inequalities

Explore
Learning 
 Linear Inequalities in Two Variables  Activity A  Find the solution set to a linear inequality in two variables using the graph of the linear inequality. Vary the terms of the inequality and vary the inequality symbol. Examine how the boundary line and shaded region change in response.
 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.
 Systems of Linear Inequalities (Slopeintercept form)  Activity A  Compare a system of linear inequalities to its graph. Vary the coefficients and inequality symbols in the system and explore how the boundary lines, shaded regions, and the intersection of the shaded regions change in response.

Websites 
 Interactive Notes: Graphing Systems of Inequalities  lessons
and practice problems at Regentsprep.org
 Interactive Notes: Review Systems of Inequalities
 Interactive Notes: Introduction to system of Inequalities
 Graphing
Systems of Inequalities

Old Website Links 

Common Core
Standards 
ACED.1 
ACED.3 
AREI.3 
AREI.12 
