Course 3 Online!
Henrico County Public Schools, Virginia
Important News: Effective August 15, 2018, this site will be realigning to the 2016 SOL.
As a result, many of the instructional notes, activities, and worksheets will be removed. Please download any files you wish to keep for future use.
8.15b - Two-Step Linear Inequalities
Number and Number Sense, Computation and Estimation

Measurement and Geometry

Probability, Statistics, Patterns, Functions, and Algebra

SOL Review Materials
Patterns, Functions, and Algebra
Focus: Linear Relationships

The student will
b)   solve two-step linear inequalities and graph the results on a number line.  
Essential Knowledge and Skills 
  • Solve two-step inequalities in one variable by showing the steps and using algebraic sentences.
  • Graph solutions to two-step 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
  1. SOL 6.18 - solve one-step linear equations in one variable
  2. SOL 7.14ab - a) solve one- and two-step linear equations; b) solve practical problems in one variable
  3. 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)
  4. 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 real-world problems involving equations and systems of equations
Instructional Materials
  1. VDOE Enhanced Scope and Sequence Lesson: Solving and Graphing Inequalities (PDF) - Solving and graphing inequalities (Word)
  2. Notes: Inequalities (flipchart)
  3. Activity: Solving Inequalities (doc)
  4. Activity: Solving Inequalities Matching (doc)
Real World Lessons
  1. Worksheet: Inequalities Practice (doc)
  2. Worksheet: Equations and Inequalities Review (doc)
  3. Worksheet: Multi-Step Inequalities Word Problems (doc)
  4. Worksheet: Solving Inequalities Web Recording Sheet (doc)
  1. SOL 8.15 Mini-Quiz: Equations, Inequalities, and Properties
  1. PH Solving Two-Step Inequalities
Explore Learning
  1. Solving Linear Inequalities using Addition and Subtraction: Solve a linear inequality. Graph the solution on a dynamic number line.
  2. Solving Linear Inequalities using Multiplication and Division: Solve an inequality involving multiplication and division. Graph the solution on a number line.
  3. 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.
  1. Interactive Notes: Solving Inequalities - lessons and practice problems at
  2. Interactive Notes: Solving two step inequalities - notes and workout problems from
VDOE Interventions
  1. 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)
  2. 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