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
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 real-world 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 real-world 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.
  • Real-world 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
  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: Greetings - Equations and Inequalities (PDF) - Writing a function to describe an inequality and solving the inequality (Word)
  2. VDOE ESS Lesson: Inequalities - Equations and Inequalities (PDF) - Relating the graphing of a line to solving an inequality in one variable (Word)
  3. Notes: Solving Inequalities (doc) | Answer Key (pdf)
Real World Lessons
  1. VDOE ESS: Solving Inequalities in One and Two Variables Worksheet (pdf)
  2. VDOE ESS: Solving Inequalities Puzzle (pdf)
  3. Worksheet: Solving Inequalities Maze (doc)
  4. Worksheet: Solving Inequalities (doc)
  5. Worksheet: Applications of Inequalities Classwork (doc)
  6. Worksheet: Applications of Inequalities Homework (doc)
  7. ExamView Quiz: Solving Multi-Step Inequalities
  8. Prentice Hall Quiz
  1. SOL Mini Quiz
  1. 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.
  2. JMU Pivotal Question: Creating Inequalities (doc)
  3. JMU Pivotal Questions: Solving Inequalities via Graphing (doc)
  4. JMU Pivotal Questions: Justifying Steps When Solving Inequalities (doc)
  5. JMU Pivotal Questions: Real World Inequalities (doc)
  1. Video: PH Solving Two-Step Inequalities
  2. Video: PH Solving Multi-Step Inequalities with Distributive
  3. Video: PH Solving Multi-Step Inequalities with Variables on Both Sides
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: Solving Inequalities - lessons and practice problems at
  2. Interactive Notes: Solving two step inequalities - notes and workout problems from
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Common Core Standards