Virginia SOL 7.PFA.4.a
The Standard
Apply properties of real numbers and the addition, subtraction, multiplication, and division properties of inequality to solve one- and two-step inequalities in one variable. Coefficients and numeric terms will be rational.
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 isolate the variable by undoing operations in reverse order while making the same change to both sides. They reverse the inequality symbol when multiplying or dividing by a negative number, including with fractions and decimals.
What Mastery Looks Like
- A student correctly isolates the variable in one or two steps when coefficients include integers, fractions, or decimals. They explain each move, reverse the symbol when needed, and check a solution value in the original inequality.
Common Misconceptions
- Students may reverse the inequality symbol after adding or subtracting, rather than only after multiplying or dividing by a negative. Some forget to reverse it when dividing by a negative coefficient. Errors with fraction and decimal operations can also lead to incorrect solutions.
How to Assess It
- Exit ticket: Solve −3/4x + 2 > 8, show each step, graph the solution, and name one value that makes the inequality true.
Lesson moves
Ways to Teach It
Use a balance mat and integer chips to model 2x − 3 < 5, then remove equal amounts from both sides.
Have students explain why the symbol reverses when both sides of −2x < 6 are divided by −2, using a number line.
Give pairs cards showing inequalities, solutions, and number-line graphs, then have them race to build matching sets.
Present a phone plan charging $15 plus $0.08 per text, with a $25 limit, and have students find the maximum texts.
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Printable 7.PFA.4.a Worksheet
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