One, None or Infinite Solutions: Notes and Practice

About this resource

What's inside this resource

Guided notes walk students through identifying whether a linear equation has one solution, no solution, or infinitely many solutions by simplifying both sides and comparing the leftover variable and constant terms. A categorizing practice sheet sorts twelve equations into the three solution types, six practice problems ask students to solve for x once they determine how many solutions exist, and an eight-question multiple-choice test-practice section includes items that ask students to identify the exact step where an error occurred in a worked-out solution. The file states it was built to meet a specific eighth-grade linear-equations standard, and every notes page, practice set, and test has a matching completed answer key later in the file.

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
Identify an error in a peer's or a sample worked solution to a linear equation

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

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.

Good to know

Questions teachers ask about this resource

What determines whether an equation ends up with one, no, or infinite solutions once both sides are simplified?

Comparing the leftover variable and constant terms: different variable terms give one solution, the same variable terms with different constants give no solution, and identical variable and constant terms give infinite solutions.

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Curriculum

Standards, concepts & topics

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

linear equations
one solution
no solution
infinite solutions
algebra

Topics

multi-step equations one none infinite solutions notes practice solving linear equations with infinite and no solution practice one solution no solution infinite solutions worksheet with answers equation with one solution one solution no solution infinite solution worksheet

More to explore

Equations with One, None or Infinite Solutions - Notes and Practice

What's inside this resource