CCSS.Math.Content.8.EE.C.7b
The Standard
Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.
Common Core State Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students simplify both sides by distributing, combining like terms, and clearing fractions when helpful. They use inverse operations to isolate the variable and check the result in the original equation.
What Mastery Looks Like
- Students choose efficient steps and keep both sides balanced. They reach the correct value, show clear work, and verify it by substituting into the original equation.
Common Misconceptions
- Students may distribute to the first term only or lose a negative sign. They may combine unlike terms, clear only some denominators, or perform an operation on just one side.
How to Assess It
- Ask students to solve and verify: (2/3)(3x − 6) + x = (1/2)(2x + 4) + 6. Require each simplifying step and a substitution check.
Lesson moves
Ways to Teach It
Use algebra tiles to model 3(x − 2) + 2x = 14, then match each tile move to an algebraic step.
Have students compare clearing fractions first with distributing first, then explain which method makes a given equation easier.
Run an error-analysis card sort where students match incorrect solutions to errors such as incomplete distribution, sign mistakes, or unequal operations.
Compare taxi fares of $3 plus $1.50 per mile and $6 plus $1.00 per mile, then find when the costs match.
Free download
Printable 8.EE.C.7b Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.8.EE.C.7b, 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.7.EE.A.1
Solving these equations requires distributing, expanding, and combining linear expressions with rational coefficients before isolating the variable.
- CCSS.Math.Content.7.NS.A.3
Solving equations with rational coefficients requires fluent rational number arithmetic when simplifying, distributing, combining terms, and isolating the variable.
- CCSS.Math.Content.7.EE.B.4a
Solving one-variable equations with rational numbers and distributive steps is required before handling multi-step equations with like terms.
What This Unlocks
Mastery here sets students up for these next.
- CCSS.Math.Content.8.EE.C.8b
Algebraic methods for systems often reduce to one linear equation requiring distributing, combining like terms, and solving with rational coefficients.
- CCSS.Math.Content.HSA-REI.B.3
Students extend solving multi-step linear equations with distribution and like terms to inequalities and letter coefficients.
Keep exploring
Related Standards
- CCSS.Math.Content.HSA-REI.A.2
Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.
- 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...
Turn this exact standard into a lesson
Grade, subject, topic, and the complete standard are prefilled. Create one free, no account needed.