Virginia SOL 7.PFA.4.b
The Standard
Investigate and explain how the solution set of a linear inequality is affected by multiplying or dividing both sides of the inequality statement by a rational number less than zero.
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 equivalent inequalities before and after scaling by a negative rational number. They reverse the inequality symbol, test values, and use number line graphs to explain why the solution sets match.
What Mastery Looks Like
- A student correctly changes < to >, ≤ to ≥, and vice versa when multiplying or dividing by a negative number. They solve and graph examples with negative integers, fractions, and decimals, then justify the reversal with a test value.
Common Misconceptions
- Students may keep the inequality symbol unchanged after multiplying or dividing by a negative number. Others reverse it when adding or subtracting a negative number, or forget to reverse it for negative fractions and decimals.
How to Assess It
- Exit ticket: Solve −3x > 12, graph the solution, and explain why the inequality symbol changes. Require one test value that confirms the solution.
Lesson moves
Ways to Teach It
Place integer cards satisfying x < 3 on a floor number line, multiply each value by −2, then observe and explain the reversed order.
Ask, “Why must −2x > 8 become x < −4?” Students justify their answers using x = −5 and x = 0.
Run a card sort matching inequalities, equivalent transformed forms, graphs, and error cards where the inequality symbol was not reversed.
A submarine descends 4 meters per minute; students solve −4t ≤ −28 to find when it reaches 28 meters below sea level.
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Related Standards
- 8.PFA.5.a
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...
- 7.PFA.4.a
Apply properties of real numbers and the addition, subtraction, multiplication, and division properties of inequality to solve one- and two-step inequalities in...
- 6.CE.1.c
Investigate and explain the effect of multiplying or dividing a fraction, whole number, or mixed number by a number between zero and one.*
- 6.PFA.4.d
Use substitution or a number line graph to justify whether a given number in a specified set makes a linear inequality in one variable true.
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