Algebra 1 Online!
Henrico County Public Schools, Virginia
Expressions and Operations

Equations and Inequalities



SOL Review Materials
The student will solve multistep linear inequalities in two variables, including
c)   solving real-world problems involving inequalities; and
d)   solving systems of inequalities.
Essential Knowledge and Skills 
  • Solve real-world 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.
  • Real-world problems can be modeled and solved using linear inequalities.
  • Set builder notation may be used to represent solution sets of inequalities.
Vertical Articulation
  1. SOL 7.15 - a) solve one-step inequalities; b) graph solutions on number line
  2. SOL 8.15 - b) solve two-step linear inequalities and graph results on number line; c) ID properties of operations used to solve
  3. SOL AFDA.5 - determine opt values in problem situations by identifying constraints/using linear programming techniques
  4. SOL AII.5 - solve nonlinear systems (algebraically/ graphically)
Instructional Materials
  1. VDOE ESS Lesson: Graphing Systems of Inequalities - Equations and Inequalities (PDF) - Graphing systems of inequalities (Word)
  2. Notes: Graphing Systems of Inequalities (ppt)
Real World Lessons
  1. VDOE ESS: Solving Inequalities in One and Two Variables Worksheet (pdf)
  2. VDOE ESS: Graphing Systems of Inequalities Worksheet (pdf) | Answer Key (pdf)
  3. VDOE ESS: What Can I Buy Worksheet (pdf)
  4. Worksheet: Solving Systems of Inequalities CW (doc)
  5. Worksheet: Solving Systems of Inequalities HW (doc)
  6. ExamView Quiz: Solving Systems of Inequalities by Graphing
  7. ExamView: Systems of Inequalities Quiz
  8. Prentice Hall Quiz - Systems of Inequalities
  1. JMU Pivotal Question: System of Inequalities Graph (doc)
  2. JMU Pivotal Question: System of Inequalities Graph #2 (doc)
  1. Video: PH Graphing Systems of Linear Inequalities
  2. Video: PH Writing Systems of Linear Inequalities
  3. Video: PH Using a System of Linear Inequalities
  4. Video Tutor - Solving a System of Linear Inequalities
Explore Learning
  1. 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.
  2. Solving Linear Inequalities using Addition and Subtraction - Solve a linear inequality. Graph the solution on a dynamic number line.
  3. Solving Linear Inequalities using Multiplication and Division - Solve an inequality involving multiplication and division. Graph the solution on a number line.
  4. Systems of Linear Inequalities (Slope-intercept 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.
  1. Interactive Notes: Graphing Systems of Inequalities - lessons and practice problems at
  2. Interactive Notes: Review Systems of Inequalities
  3. Interactive Notes: Introduction to system of Inequalities
  4. Graphing Systems of Inequalities
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Common Core Standards