CCSS.Math.Content.HSA-REI.B.3
The Standard
Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
Common Core State Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students isolate the variable while keeping both sides equivalent. They solve and graph inequalities, reverse the sign when needed, and rearrange equations containing letter coefficients.
What Mastery Looks Like
- Students show valid steps, simplify accurately, and check a solution by substitution. They graph inequality solutions correctly and state restrictions when dividing by a letter.
Common Misconceptions
- Students may distribute a negative sign incorrectly or combine unlike terms. They often forget to reverse the inequality sign after multiplying or dividing by a negative number. Some divide by a letter without stating that it cannot equal zero.
How to Assess It
- Give an exit ticket: solve 3(2x - 5) ≤ 9, then solve ax + b = c for x and state the needed restriction.
Lesson moves
Ways to Teach It
Use a balance mat and algebra tiles to model 2x + 3 = 11, then record each matching move as an equation step.
Ask students to explain why dividing both sides of an inequality by a negative number reverses the inequality sign.
Run a card match pairing equations and inequalities with worked solutions, including symbolic forms such as ax + b = c.
Give a phone plan with a monthly fee and per-gigabyte charge, then ask students to find usage within a set budget.
Free download
Printable HSA-REI.B.3 Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.HSA-REI.B.3, with an answer key for the teacher on its own page. No account needed.
PDF, US Letter, prints cleanly in black and white.
Download the worksheetLearning progression
Where This Standard Sits
Before This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.8.EE.C.7
Students extend one-variable equation solving to inequalities and literal coefficients, using the same inverse operations and solution reasoning.
- CCSS.Math.Content.8.EE.C.7b
Students extend solving multi-step linear equations with distribution and like terms to inequalities and letter coefficients.
- CCSS.Math.Content.7.EE.B.4b
Solving and graphing simple one-variable inequalities supports later symbolic inequality solving with more general coefficients and forms.
What This Unlocks
Mastery here sets students up for these next.
- CCSS.Math.Content.HSA-CED.A.4
Rearranging a formula is solving an equation for a chosen variable, using inverse operations and handling letter coefficients.
- CCSS.Math.Content.HSA-REI.A.2
Solving rational and radical equations requires isolating expressions and solving resulting one-variable linear equations after clearing denominators or roots.
- CCSS.Math.Content.HSA-REI.B.4a
Completing the square and deriving the formula require fluent equivalent equation moves with variables and literal coefficients.
- CCSS.Math.Content.HSA-REI.D.12
Solving one-variable inequalities supports rearranging two-variable inequalities and understanding which side of a boundary satisfies the inequality.
Keep exploring
Related Standards
- CCSS.Math.Content.HSA-REI.B
Solve equations and inequalities in one variable
- CCSS.Math.Content.HSA-CED.A.1
Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rati...
- CCSS.Math.Content.6.EE.B
Reason about and solve one-variable equations and inequalities.
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