Worksheets · Pre-Algebra

Pre-Algebra multi-step inequalities worksheet

Everything from the multi-step equation sheet, with the extra rule that dividing by a negative turns the sign round. Collecting the variable on the positive side is often the easier route.

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 Inequalities

Date Period

Solve each inequality.

  1. 3a+7a−9<71
  2. −2p−7>−p−3
  3. 5(b−2)<−30
  4. 5a+9a−7≤21
  5. −7n−1>2n+17
  6. 3(a−6)≥−42
  7. 9y−y+2≥66
  8. −7k+2≤2k−52
  9. 4(m+1)<−8
  10. −9k−2k+5≥27
  11. −7m+5<2m+14
  12. 5(b−2)≥−50
  13. x−8x+7≥49
  14. 8b−4<7b−8
  15. 2(m−1)<−18
  16. −8x−9x+4≥38
  17. 8a+6>−2a−44
  18. 3(x−5)>−36
  19. 2x−8x−7≥−37
  20. b+1≤−2b−14

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

Sigma Prep · sigmaprep.io/worksheets

Name

Multi‑Step InequalitiesAnswer keyVersion 1

Date Period

Solve each inequality.

  1. 3a+7a−9<71a<8
  2. −2p−7>−p−3p<−4
  3. 5(b−2)<−30b<−4
  4. 5a+9a−7≤21a≤2
  5. −7n−1>2n+17n<−2
  6. 3(a−6)≥−42a≥−8
  7. 9y−y+2≥66y≥8
  8. −7k+2≤2k−52k≥6
  9. 4(m+1)<−8m<−3
  10. −9k−2k+5≥27k≤−2
  11. −7m+5<2m+14m>−1
  12. 5(b−2)≥−50b≥−8
  13. x−8x+7≥49x≤−6
  14. 8b−4<7b−8b<−4
  15. 2(m−1)<−18m<−8
  16. −8x−9x+4≥38x≤−2
  17. 8a+6>−2a−44a>−5
  18. 3(x−5)>−36x>−7
  19. 2x−8x−7≥−37x≤5
  20. b+1≤−2b−14b≤−5

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

How to do these

5−3x<2x−15

  1. Add 3x to both sides to keep the x term positive: 5 < 5x - 15.
  2. Add 15: 20 < 5x.
  3. Divide by 5: 4 < x, which is x > 4.

The answer is x>4.

Where students go wrong

Losing track of which side the variable ended on. 4 < x and x > 4 say the same thing, and students who read the first one left to right write x < 4. Rewrite it with the variable in front before answering.

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

What you can put on this worksheet

Like terms to collect
−6v−9v−8≤−23 → v≥1
The variable on both sides
−6v−8≤−9v−5 → v≤1
Parentheses to expand
−4(v−8)≤28 → v≥1

Questions about these worksheets

Yes. Every multi-step inequalities 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 inequalities 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 3: like terms to collect, the variable on both sides and parentheses to expand. Tick as many as you want and set how many of each, or let it spread them evenly.

Losing track of which side the variable ended on. 4 < x and x > 4 say the same thing, and students who read the first one left to right write x < 4. Rewrite it with the variable in front before answering.