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

Equations and Inequalities



SOL Review Materials
The student will solve multistep linear and quadratic equations in two variables, including
b)   justifying steps used in simplifying expressions and solving equations, using field properties and axioms of equality that are valid for the set of real numbers and its subsets;
d)   solving multistep linear equations algebraically and graphically;
f)   solving real-world problems involving equations and systems of equations.
Graphing calculators will be used both as a primary tool in solving problems and to verify algebraic solutions.
Essential Knowledge and Skills 
  • Solve equations, using the field properties of the real numbers and properties of equality, to justify simplification and solution.
  • Solve multistep linear equations in one variable.
  • Confirm algebraic solutions to linear equations, using a graphing calculator.
  • Determine if a linear equation in one variable has one, an infinite number, or no solutions.
Essential Understandings
  • A solution to an equation is the value or set of values that can be substituted to make the equation true.
  • The solution of an equation in one variable can be found by graphing the expression on each side of the equation separately and finding the x-coordinate of the point of intersection. 
  • Real-world problems can be interpreted, represented, and solved using linear equations.
  • The process of solving linear equations can be modeled in a variety of ways, using concrete, pictorial, and symbolic representations.
  • Properties of real numbers and properties of equality can be used to justify equation solutions and expression simplification.
  • Equations can be used as mathematical models for real-world situations.
  • Set builder notation may be used to represent solution sets of equations.
Vertical Articulation
  1. SOL 7.14 - a) solve one- and two-step linear equations; b) solve practical problems in one variable
  2. SOL 7.16 - apply properties w/ real numbers: a) commutative and associative properties for add/multi; b) distributive property; c) add/multi identity properties; d) add/multi inverse properties; e) multi property of zero
  3. SOL 8.15 - a) solve multistep linear equations in one variable (variable on one and two sides of equations); c) ID properties of operations used to solve
  4. SOL AII.3 - perform operations on complex numbers/express results in simplest form using patterns of the powers of i/ID field properties for complex numbers
  5. SOL AII.4 - solve (algebraically/graphically) a) absolute value equation/inequalities; b) quadratic equations over complex; c) equations containing rational algebraic expression; d) equations containing radical expressions
Instructional Materials
  1. VDOE ESS Lesson: Solving Linear Equations - Equations and Inequalities (PDF) - Exploring the functions of the graphing calculator; solving multistep linear equations (Word)
  2. Notes: Solving Equations with Variables on Both Sides (doc) | Answer Key (pdf)
Real World Lessons
  1. Worksheet: Solving Equations with Variables on Both Sides CW (doc)
  2. Worksheet: Solving Equations with Variables on Both Sides CW (doc)
  3. Quiz: Solving Equations with Variables on Both Sides (doc)
  4. ExamView Quiz: Solving Multi-Step Equations
  5. ExamView Quiz: Solving Equations with Variables on Both Sides
  6. Prentice Hall Quiz #1
  7. Prentice Hall Quiz #2
  8. Prentice Hall Quiz #3
  1. SOL Mini Quiz
  1. Video: PH Solving Two-Step Equations
  2. Video: PH Writing and Solving Two-Step Equations
  3. Video: PH Solving Equations with Variables on Both Sides
  4. Video: PH Consecutive Integers Problem
  5. Video: PH Solving Distance, Rate, Time Problems
Explore Learning
  1. Solving Formulas for any Variable - Choose the correct steps to solve a formula for a given variable. Use the feedback to diagnose incorrect steps.
  2. Modeling and Solving Two-Step Equations - Solve a two‑step equation using a cup‑and‑counter model. Use step‑by‑step feedback to diagnose and correct incorrect steps.
  3. Solving Equations By Graphing Each Side - Solve an equation by graphing each side and finding the intersection of the lines. Vary the coefficients in the equation and explore how the graph changes in response.
  4. Solving Two-Step Equations - Choose the correct steps to solve a two-step equation. Use the feedback to diagnose incorrect steps.
  1. Interactive Notes: Solve Linear Equations - lessons and practice problems at
  2. Notes: Visual Equations - lesson on solving equations visually using tiles from
  3. Interactive Notes: Algebra Balance Scales - (Needs Internet Explorer browser) Interactive math manipulative that solves equations using a balance beam representation Choose the Algebra Balance Scales icon from the list.
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Common Core Standards