A.5abc 
The student will solve multistep linear inequalities in two variables, including
a) solving multistep linear inequalities algebraically and graphically;
b) justifying steps used in solving inequalities, using axioms of inequality and properties of order that are valid for the set of real numbers and its subsets;
c) solving realworld problems involving inequalities.


Essential Knowledge and Skills 
 Solve multistep linear inequalities in one variable.
 Justify steps used in solving inequalities, using axioms of inequality and properties of order that are valid for the set of real numbers.
 Solve realworld problems involving inequalities.

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.
 Properties of inequality and order can be used to solve 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: Greetings  Equations and Inequalities (PDF)  Writing a function to describe an inequality and solving the inequality (Word)
 VDOE ESS Lesson: Inequalities  Equations and Inequalities (PDF)  Relating the graphing of a line to solving an inequality in one variable (Word)
 Notes: Solving Inequalities (doc)  Answer Key (pdf)

Real World Lessons 

Practice 
 VDOE ESS: Solving Inequalities in One and Two Variables Worksheet (pdf)
 VDOE ESS: Solving Inequalities Puzzle (pdf)
 Worksheet: Solving Inequalities Maze (doc)
 Worksheet: Solving Inequalities (doc)
 Worksheet: Applications of Inequalities Classwork (doc)
 Worksheet: Applications of Inequalities Homework (doc)
 ExamView Quiz: Solving MultiStep Inequalities
 Prentice Hall Quiz

SelfAssessments 
 SOL Mini Quiz

Skills 
 Mathematics Assessment Project: A15:Multiple Solutions  In this task, you will look at a number of equations and inequalities that have more than one solution.
 JMU Pivotal Question: Creating Inequalities (doc)
 JMU Pivotal Questions: Solving Inequalities via Graphing (doc)
 JMU Pivotal Questions: Justifying Steps When Solving Inequalities (doc)
 JMU Pivotal Questions: Real World Inequalities (doc)

Videos 
 Video: PH Solving TwoStep Inequalities
 Video: PH Solving MultiStep Inequalities with Distributive
 Video: PH Solving MultiStep Inequalities with Variables on Both Sides

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

Old Website Links 

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