11 questions
8th - 8th Grade
Mathematics
This Grade 8 mathematics worksheet focuses on classifying linear equations as having one solution, no solution, or infinitely many solutions. Students simplify equations by combining like terms, using the properties of equality, and applying the distributive property before deciding whether the variable has one value, disappears in an identity, or produces a contradiction. Some fill-in-the-blank items also require students to enter a numerical solution when an equation has one solution. The worksheet uses multiple-choice and fill-in-the-blank questions with equations such as 3x + 15 = 3(x + 5), 4x + 8 = 2(2x + 4), and equations involving constants and variable terms on both sides. It is designed for Grade 8 math instruction, guided practice, review, or a quick check of students’ understanding of special cases in linear equations. This free printable worksheet includes a complete answer key for efficient checking and feedback.
Worksheet settings
Font size
WorksheetsAnswer KeyNo Solutions
No Solution
Infinitely Many Solutions
No Solutions
No Solution
infinitely many
Infinitely many solutions
This Grade 8 worksheet asks students to simplify linear equations and classify them as having one solution, no solution, or infinitely many solutions. Multiple-choice items focus on recognizing identities such as 3x + 15 = 3(x + 5) and contradictions such as −5 + 7x = 7x + 5, while fill-in-the-blank items require students to enter a specific solution when appropriate.
Model an equation from the worksheet by simplifying both sides and discussing what remains after like terms are combined. Have students explain whether the result isolates a variable, creates a false statement, or creates a true statement for every value of the variable; then use the multiple-choice items for guided practice and the fill-in items for independent solving.
Students may confuse a true identity with no solution, even though an equation such as 3x − 3 = −3 + 3x is true for every value of x. They may also stop after canceling variable terms, fail to distribute a negative or a factor, or enter a value such as −2 without recognizing that the fill-in response asks for the equation’s solution.
This worksheet is available as a printable PDF and as a digital quiz on Wayground, and it includes a complete answer key. You can grade printed submissions by scanning student work with the Wayground for Teachers app, or use the digital version for online response collection and grading.
Use the worksheet’s Advanced Settings to adjust font spacing or choose a larger font size so the equations and answer choices are easier to scan. You can also enable a dyslexia-friendly font or translate the worksheet into another language when that supports students working through the equation-classification and fill-in items.
Wayground offers a comprehensive collection of free printable worksheets and practice problems across subjects, with downloadable PDFs and answer keys to support mastery of essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.