CCSS.Math.Content.8.EE.C.7a
The standard
Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).
Common Core State Standards for Mathematics
What this standard means
Students need to solve linear equations in one variable and decide whether the equation has one solution, no solution, or infinitely many solutions. They should use legal equation moves, like distributing, combining like terms, and doing the same operation to both sides, until the equation clearly shows the outcome.
Mastery looks like a student saying, “This becomes x = 4, so one solution,” or “This becomes 7 = 7, so all values work.” Common sticking points are sign errors, dropping terms when distributing, and thinking every equation must have one answer even when variables cancel out.
Ways to teach it
- Use algebra tiles or paper balance mats to model 3x + 2 = x + 10, then record each matching symbolic step.
- Ask students to write one equation with one solution, one with no solution, and one with infinite solutions, then explain how they know.
- Give three mini equations where variables cancel, and have students label each as one solution, no solution, or infinite solutions.
- Connect to phone plans by comparing two cost expressions and deciding if they match at one month, never, or for every month.
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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...
- CCSS.Math.Content.8.EE.C.7
Solve linear equations in one variable.
- CCSS.Math.Content.HSA-REI.B.3
Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.