Worksheets · Algebra 1

One-step inequalities worksheet

One operation to undo. Easy keeps every number positive; from medium up, half of them divide by a negative, and that is the only case where the inequality sign changes direction. Hard divides by a fraction or a decimal instead.

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

One‑Step Inequalities

Date Period

Solve each inequality.

  1. −8a<−160
  2. r−9>1
  3. b+6<4
  4. −4n<48
  5. −10a≤−40
  6. y−5<−1
  7. n−13≤−10
  8. k−14<1
  9. 3y≥57
  10. 9x≥−162
  11. −6n≤−18
  12. 2n>−28
  13. k+6≥2
  14. n−2≤5
  15. 4m≤12
  16. −4r>−80
  17. −4x≥60
  18. k−9≥−4
  19. 8v>56
  20. a−19<−26

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

Sigma Prep · sigmaprep.io/worksheets

Name

One‑Step InequalitiesAnswer keyVersion 1

Date Period

Solve each inequality.

  1. −8a<−160a>20
  2. r−9>1r>10
  3. b+6<4b<−2
  4. −4n<48n>−12
  5. −10a≤−40a≥4
  6. y−5<−1y<4
  7. n−13≤−10n≤3
  8. k−14<1k<15
  9. 3y≥57y≥19
  10. 9x≥−162x≥−18
  11. −6n≤−18n≥3
  12. 2n>−28n>−14
  13. k+6≥2k≥−4
  14. n−2≤5n≤7
  15. 4m≤12m≤3
  16. −4r>−80r<20
  17. −4x≥60x≤−15
  18. k−9≥−4k≥5
  19. 8v>56v>7
  20. a−19<−26a<−7

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

How to do these

−4x>12

  1. Divide both sides by -4.
  2. Dividing by a negative turns the sign round.
  3. So the answer points the other way.

The answer is x<−3.

Where students go wrong

Forgetting to turn the sign round. -4x > 12 gives x < -3, not x > -3, and the quickest way to catch it is to test a number: x = -10 works, x = 0 does not.

Also called solving simple inequalities.

Questions about these worksheets

Yes. Every one-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.

Algebra 1 is usually taken around 8th or 9th 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 one-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.

Forgetting to turn the sign round. -4x > 12 gives x < -3, not x > -3, and the quickest way to catch it is to test a number: x = -10 works, x = 0 does not.