Virginia SOL 7.PFA.4.h
The Standard
Describe the differences and similarities between solving linear inequalities in one variable and linear equations in one variable.
Virginia Standards of Learning for Mathematics · The student will write and solve one- and two-step linear inequalities in one variable, including problems in context, that require the solution of a one- and two-step linear inequality in one variable.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students compare the steps used to isolate a variable in equations and inequalities. They explain how the answers differ and when an inequality symbol must reverse. They connect inequality solutions to number line graphs.
What Mastery Looks Like
- Students use inverse operations correctly for both equations and inequalities. They explain that an equation often gives one value, while an inequality gives a set of values. They reverse the inequality symbol only when multiplying or dividing by a negative number.
Common Misconceptions
- Students may reverse the inequality symbol after adding or subtracting a negative number. Others forget to reverse it when multiplying or dividing by a negative number. Some give one value instead of a solution set or graph only the boundary point.
How to Assess It
- Give the exit ticket: Solve −2x + 3 = 11 and −2x + 3 ≤ 11. Explain one similarity and two differences in the work and answers.
Lesson moves
Ways to Teach It
Use algebra tiles to solve paired equation and inequality cards, then place each result on a number line.
Write three similarities and two differences between solving 4x + 3 = 19 and 4x + 3 < 19.
Play a card sort matching inequalities, solution steps, graphs, and explanations of when the inequality symbol reverses.
Compare a fixed $25 budget equation with a spending limit inequality, and identify what each solution means.
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Related Standards
- 7.PFA.4
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- 8.PFA.5.g
Interpret algebraic solutions in context to linear inequalities in one variable.
- 7.PFA.3
The student will write and solve two-step linear equations in one variable, including problems in context, that require the solution of a two-step linear equati...
- 7.PFA.4.d
Write one- or two-step linear inequalities in one variable to represent a verbal situation, including those in context.
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