Small practice
brighter futures.
Checking sign-in status
Menu

Equations practice

Determining equation solution types worksheets

Classify twelve linear equations as having no solutions, one solution or infinitely many solutions. Choose any nonempty combination, with exact rational roots on separate keys.

Ready-made English PDF · fixed settings

Worksheet · LetterWorksheet · A4
Customize worksheet ↓
With answer key

Customization below makes a separate PDF.

First page of the determining equation solution types worksheets printable worksheetOpen full-size sample (first page)

Fixed English ready-made files. Custom settings below apply only to the configured PDF.

Ready to print

Start with a ready-made worksheet

Simplify both sides and classify each equation. If it has one solution, solve it exactly.

Download the practice pages alone, or include a separate answer key or teacher model. Longer activities may use more than one page.

US Letter

Student worksheetWorksheet with answers

A4

Student worksheetWorksheet with answers
Customize this worksheet

Paper sizes and printing help · More equations activities

Simplify both sides before classifying the equation

A variable coefficient that cancels from both sides leaves either a true statement, with infinitely many solutions, or a false statement, with no solutions. When the coefficients differ, the equation has one exact solution.

Every sheet has twelve shuffled equations in two sections. Selected solution types appear equally often, and the equations include grouped distribution, negated groups, repeated variable terms and variables on both sides. Unique roots remain exact fractions.

Learning objective

What this activity builds

Simplify both sides of a linear equation and use the resulting coefficients and constants to identify its complete solution set.

Worked example

Classify 3(x + 2) = 3x + 6.

Infinitely many solutions.

Distribution gives 3x + 6 = 3x + 6. Both sides are equivalent for every value of x, so the equation is an identity.

Teaching notes

Make the practice count

  • Simplify each side before moving any terms.
  • If the variable terms cancel, compare the remaining constants.
  • A true constant statement means infinitely many solutions.
  • A false constant statement means no solutions.
  • Keep a unique noninteger root as a reduced fraction.

Make it yours

Customize the practice

Choose your options, update the preview, then download the exact same pages.

Choose one or more solution types. Every twelve-question sheet balances the selected types and includes distribution, negation, repeated terms and variables on both sides.

Worksheet settings

Solution types
Page note and reproducible seed

The same settings and seed make the same questions. Shared links include your page note; leave personal information out. Notes use the selected language’s supported characters; English accepts basic Latin text.

Configured PDF · Determining Equation Solution Types · US Letter

Preview ready. Download includes these exact pages.

1 student page
Enlarged pages scroll. PDF size stays the same.
Math SheetNameScore/ 12TeacherDateDetermining Equation Solution TypesClassify each equation. If it has one solution, solve it exactly.Equations 1–61.5f-f-9=f+3f-92.-5z+1=-8z+133.-6c+3c-2=-31c+94.-(3m-2)+5=m-4m+75.-15q=-8q-7q-56.-(2s-2)+6=-2s-1Equations 7–127.-3(2g+6)-17=g-7g-358.-3m-11=2m+299.y-3y+13=-2y+1310.-(-4y+5)+5=-50y+4711.4(-6k+3)+6=-24k+1712.-20x-33=2(-10x-8)-12math-sheet.comPage 1 / 1

A useful next step

Related activities

First page preview: Variables on both sides equations worksheets

Equations

Variables on both sides equations worksheets

Solve ten equations with the same variable on both sides. Choose the letter policy, constant and coefficient ranges, and signed or positive-only operands, with full worked solutions.

Preview and download
First page preview: Multi-step integer equations worksheets

Equations

Multi-step integer equations worksheets

Choose from eleven equation structures for ten questions with integer operands. Practice like terms, grouped expressions and variables on either side, with exact worked solutions and separately rounded answers.

Preview and download
First page preview: Solving quadratics by factoring worksheets

Equations

Solving quadratics by factoring worksheets

Solve ten factorable quadratic equations with complete exact root sets. Choose factored form, expanded form, rearrangement practice or a balanced mixed sheet.

Preview and download