Virginia SOL 8.PFA.5.a
The Standard
Apply properties of real numbers and properties of inequality to solve multistep linear inequalities (up to four steps) in one variable with the variable on one or both sides of the inequality. Coefficients and numeric terms will be rational. Inequalities may contain expressions that need to be expanded (using the distributive property) or require combining like terms to solve.
Virginia Standards of Learning for Mathematics · The student will write and solve multistep linear inequalities in one variable, including problems in context that require the solution of a multistep linear inequality in one variable.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students simplify expressions by distributing and combining like terms, then isolate the variable. They apply operations to both sides and reverse the inequality sign when multiplying or dividing by a negative number.
What Mastery Looks Like
- A student can simplify each side, move variable terms and constants, and isolate the variable without changing the solution set. They state the solution correctly and verify it with substitution or a number line.
Common Misconceptions
- Students often forget to reverse the inequality sign after multiplying or dividing by a negative number. They may distribute to only one term, combine unlike terms, or move terms across the sign without changing them correctly.
How to Assess It
- Give this exit ticket: Solve −2(x − 3) + 5 ≥ x − 1, show each step, and check one value from your solution set.
Lesson moves
Ways to Teach It
Give pairs transformation cards to order, including a card that flips the inequality after division by a negative number.
Ask students to explain why dividing both sides by −3 changes ≥ to ≤, using a numerical example.
Run an inequality match game where students pair problem cards with solution cards and check each match by substitution.
Have students write and solve an inequality for a phone plan with a fixed fee, per-gigabyte charge, and spending limit.
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