Worksheets · Pre-Algebra

Pre-Algebra multi-step equations worksheet

Collecting like terms, the variable on both sides, and parentheses to expand. You can also mix in equations with no solution and equations true for every number, which is the part students never see coming.

Select your difficulty

Pick more than one for a sheet that mixes them.

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Multi‑Step Equations

Date Period

Solve each equation.

  1. −4a+6a+4=−6
  2. −4y−1=−2y+7
  3. 5(m−4)=−30
  4. 3(v−15)=−4(v−1)
  5. 6p−5p−2=−5
  6. −3n+3=−6n+18
  7. 5(y+9)=30
  8. −2(y+4)=3(y−11)
  9. −3n−3n+5=41
  10. −2x−2=−9x+47
  11. 4(a−1)=−8
  12. 4(m+1)=−4(m−5)
  13. 6y−2y−7=−39
  14. 8k−2=2k−20
  15. 4(p−9)=−68
  16. 4(k−7)=−3(k+14)
  17. −2y−y−1=−13
  18. −5k−2=8k+102
  19. 5(a−8)=−55
  20. −3(a+1)=2(a−14)

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Multi‑Step EquationsAnswer keyVersion 1

Date Period

Solve each equation.

  1. −4a+6a+4=−6{−5}
  2. −4y−1=−2y+7{−4}
  3. 5(m−4)=−30{−2}
  4. 3(v−15)=−4(v−1){7}
  5. 6p−5p−2=−5{−3}
  6. −3n+3=−6n+18{5}
  7. 5(y+9)=30{−3}
  8. −2(y+4)=3(y−11){5}
  9. −3n−3n+5=41{−6}
  10. −2x−2=−9x+47{7}
  11. 4(a−1)=−8{−1}
  12. 4(m+1)=−4(m−5){2}
  13. 6y−2y−7=−39{−8}
  14. 8k−2=2k−20{−3}
  15. 4(p−9)=−68{−8}
  16. 4(k−7)=−3(k+14){−2}
  17. −2y−y−1=−13{4}
  18. −5k−2=8k+102{−8}
  19. 5(a−8)=−55{−3}
  20. −3(a+1)=2(a−14){5}

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

5p−14=8p+4

  1. Get the variable on one side: subtract 5p from both sides.
  2. That leaves -14 = 3p + 4.
  3. Subtract 4, then divide by 3.

The answer is p=−6.

Where students go wrong

Losing a minus sign when a parenthesis has a negative in front. In -(1 + 7x) both terms flip, giving -1 - 7x, and students who only flip the first get an answer that looks reasonable and is wrong. The other one is stopping too early when the variables cancel: 4m - 4 = 4m is not a mistake in your working, it is an equation with no solution.

Also called equations with variables on both sides or solving linear equations.

What you can put on this worksheet

Like terms to collect
5v−3v+3=7 → {2}
The variable on both sides
−5v+4=3v−44 → {6}
Parentheses to expand
4(v−6)=−20 → {1}
Parentheses on each side
4(v+4)=−3(v−10) → {2}
Mix in some with no solution
7v−5=7v+3 → No solution
Mix in some true for every number
4v−12=4(v−3) → All real numbers

Questions about these worksheets

Yes. Every multi-step equations sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Pre-Algebra is usually taken around 7th or 8th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the multi-step equations questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 6: like terms to collect, the variable on both sides, parentheses to expand, parentheses on each side, mix in some with no solution and mix in some true for every number. Tick as many as you want and set how many of each, or let it spread them evenly.

Losing a minus sign when a parenthesis has a negative in front. In -(1 + 7x) both terms flip, giving -1 - 7x, and students who only flip the first get an answer that looks reasonable and is wrong. The other one is stopping too early when the variables cancel: 4m - 4 = 4m is not a mistake in your working, it is an equation with no solution.