What does the answer key show?

By default, the key shows expansion and exact conversions where needed, collection and solving steps, and an explanation of each solution set. Every unique solution includes a check in the original equation. Choose Answers only for final answers without the worked steps.

How do the settings differ?

Easier has two integer solutions among its six equations. On level has one negative integer solution and one unique zero solution. Harder has one negative and one positive half-integer solution. Each setting also includes two equations with no solution and two true for all real values.

Can the notation reveal the solution type?

At the harder setting, each solution type appears once in a collection task and once in a mixed fraction and decimal task. At every setting, compare the algebra on both sides to decide the answer.

8th grade classifying linear solution sets

8th grade classifying linear solution sets worksheets

Six shuffled equations include two with one solution, two with no solution and two with all real numbers as solutions. Easier uses integer coefficients and constants. On level adds expansion and a unique zero solution. Harder requires collection on both sides and uses more opposing signs, hundredths and two noninteger solutions. Collect and compare both sides to explain each solution set.

Free printable PDF worksheet, aligned to Common Core 8.EE.C.7.a.

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The kind of problems you'll get

Work over the real numbers. Classify each equation: one solution, no solution, or infinitely many. Show your steps. Find and check any unique solution.

2 × z − 4 = 2 × z − 4
Answer: −4 = −4 True for every real value. Infinitely many solutions.
2 × (3 × p + 2) = 6 × p − 4
Answer: 4 = −4 False statement. No solution.
2 × (3 × a − 3/2) = 4 × a − 3
Answer: a = 0 One solution.

Every print pulls a fresh set of problems at this level, so a make-up test or a second sibling never gets the same sheet.

What's on an 8th grade sheet

Classifying linear solution sets. Work over the real numbers. Classify each equation: one solution, no solution, or infinitely many. Show your steps. Find and check any unique solution. 6 problems per page.

Every version prints on US Letter or A4, with its answer key after the problems.

How to teach this

Compare the variable coefficients and constants after collecting. Different coefficients lead to one solution. Equal coefficients leave a true or false constant statement. A result such as x = 0 names one value; a result such as 3 = 3 holds for every real value.

Watch for: A unique solution of zero is different from an equation that is true for every real value. When variable terms cancel, use the remaining constants to decide whether the statement is true or false. Checking one value cannot prove that every real value is a solution.

Common questions about 8th grade classifying linear solution sets

What does the answer key show?: By default, the key shows expansion and exact conversions where needed, collection and solving steps, and an explanation of each solution set. Every unique solution includes a check in the original equation. Choose Answers only for final answers without the worked steps.
How do the settings differ?: Easier has two integer solutions among its six equations. On level has one negative integer solution and one unique zero solution. Harder has one negative and one positive half-integer solution. Each setting also includes two equations with no solution and two true for all real values.
Can the notation reveal the solution type?: At the harder setting, each solution type appears once in a collection task and once in a mixed fraction and decimal task. At every setting, compare the algebra on both sides to decide the answer.

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Aligned to Common Core 8.EE.C.7.a. Reviewed by the One more sheet team. Content version 241, updated October 2026.

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