8th Grade Math · Multi-Step Equations
Number of solutions Worksheets
Free and printable, with a full answer key. Every worksheet is generated fresh, so you can hand a different version to every student.
Equations that may have one solution, no solution or infinitely many, such as 2(x + 3) = 2x + 6.
Or start with a ready-made version:
How it works: a quick refresher
For the adult at the table. These are the rules the worksheet practices, followed by one problem worked from start to finish.
| Strategy | How it works |
|---|---|
| Simplify each side first | Distribute, then combine like terms, before moving anything across. |
| Collect the variable | Add or subtract variable terms so they end up on one side: 5x − 3 = 2x + 9 → 3x − 3 = 9. |
| Then isolate it | Undo the constant, then the coefficient: 3x = 12 → x = 4. |
| No solution | If the variables cancel and leave a false statement, such as 6 = 4, there is no solution. |
| Infinitely many solutions | If the variables cancel and leave a true statement, such as 6 = 6, every number is a solution. |
Worked example
Solve −2(n − 3) = 4n + 18.
- Distribute: −2n + 6 = 4n + 18.
- Subtract 4n from both sides: −6n + 6 = 18.
- Subtract 6 from both sides: −6n = 12.
- Divide by −6: n = −2.
- Check: −2(−2 − 3) = 10, and 4(−2) + 18 = 10.
Ready-made versions
Three fixed versions you can link to or share. Each is a PDF with its own answer key.
- Number of solutions Worksheets, version 1Worksheet PDFAnswer key PDF
- Number of solutions Worksheets, version 2Worksheet PDFAnswer key PDF
- Number of solutions Worksheets, version 3Worksheet PDFAnswer key PDF
Grade level and standard
Written for 8th grade math (expressions and equations) and aligned to CCSS 8.EE.C.7. It also works as review in later grades.
Common questions
- Is there an answer key?
- Yes. Every worksheet has a matching answer key with each answer worked on the same grid or layout as the question. The worksheet ID printed at the bottom of each page pairs a sheet with its key.
- How should students write the answer when there is no single solution?
- Write “no solution” or “infinitely many solutions”. The answer key uses those words.
- Are any answers fractions?
- No. Every equation with one solution has a whole-number answer, positive or negative.
- How many different versions are there?
- About a million per skill. Each time you press the button the problems are generated fresh, so you can print a different version for every student, a retake, or another night of practice.
- Are the worksheets free?
- Yes. They are free to print and copy for your home or classroom, with no sign-up.