Equations with One, None, & Infinite Solutions NOTES & PRACTICE
- Grades
- Grade 8, Middle School
- File type
- Preparation
- Print ready
- Subject
- Math, Algebra
- Topic
- multi-step equations, one none infinite solutions
- Preparation
- Print ready
- Standards
- 8.EE.C.7
About this resource
What's inside this resource
This resource was developed to meet the requirements of the 8th Grade Expressions & Equations Standards below:
Solve linear equations in one variable.
CCSS.math.content.8.ee.c.7.a
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).
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In the classroom
Teaching tips & learning objectives
Learning objectives
Simplify both sides of a linear equation to determine the number of solutions
Categorize an equation as having one solution, no solution, or infinite solutions
Solve a multi-step linear equation for x when exactly one solution exists
Teaching tips
Give students time to generate their own example equations for each solution type before revealing the answer, as the notes page prompts
Use the categorizing practice as a quick sort activity before moving to the multi-step solve-for-x problems
Discuss the two grading-scale options the file offers for the multiple-choice test practice section, since the questions are described as more rigorous than simple recall. Give students more practice deciding whether an equation has one, no, or infinitely many solutions.
Skills covered
Solution-type identification — students simplify both sides of an equation and compare terms to classify it as one, no, or infinite solutions.
Multi-step equation solving — students solve six multi-step linear equations for x once they confirm exactly one solution exists.
Error analysis — students examine a worked solution and identify the specific step where a mistake was made.
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Curriculum
Standards, concepts & topics
Standards
Standards
- 8.EE.C.7 — Solve linear equations in one variable. a. 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). b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.
Core concepts
Core concepts
linear equations
one solution
no solution
infinite solutions
algebra
Topics
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