Worksheets · Algebra 1

Inequalities with variables on both sides worksheet

These solve exactly like equations with the variable on both sides, with one extra rule. If the step that finishes it is dividing or multiplying by a negative number, the inequality sign turns round.

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

Inequalities: Variables on Both Sides

Date Period

Solve each inequality.

  1. 4a−30<11a−170
  2. −3p−26>−p−8
  3. 12b+22<−3b−113
  4. 14r−18<−11r+232
  5. 2p+28<−p−17
  6. −10b+29≥13b−178
  7. 5k+25≥8k+28
  8. 3n−18≤−2n−3
  9. 12a−28≤−3a+2
  10. −2b−24<−b−35
  11. −12a+28<−14a+50
  12. −11x−28<2x+232
  13. −6r+17≥5r+39
  14. −6y−29≥−3y−71
  15. −11y−27<−4y−13
  16. 5m+27≥−8m+144
  17. −5x+18<−13x+122
  18. 8m−27≤2m−141
  19. −8n−15≤2n+115
  20. 4a+12<−14a+156

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

Sigma Prep · sigmaprep.io/worksheets

Name

Inequalities: Variables on Both SidesAnswer keyVersion 1

Date Period

Solve each inequality.

  1. 4a−30<11a−170a>20
  2. −3p−26>−p−8p<−9
  3. 12b+22<−3b−113b<−9
  4. 14r−18<−11r+232r<10
  5. 2p+28<−p−17p<−15
  6. −10b+29≥13b−178b≤9
  7. 5k+25≥8k+28k≤−1
  8. 3n−18≤−2n−3n≤3
  9. 12a−28≤−3a+2a≤2
  10. −2b−24<−b−35b>11
  11. −12a+28<−14a+50a<11
  12. −11x−28<2x+232x>−20
  13. −6r+17≥5r+39r≤−2
  14. −6y−29≥−3y−71y≤14
  15. −11y−27<−4y−13y>−2
  16. 5m+27≥−8m+144m≥9
  17. −5x+18<−13x+122x<13
  18. 8m−27≤2m−141m≤−19
  19. −8n−15≤2n+115n≥−13
  20. 4a+12<−14a+156a<8

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

How to do these

5x−14<8x+4

  1. Take 5x from both sides: -14 < 3x + 4.
  2. Take 4 from both sides: -18 < 3x.
  3. Divide by 3, which is positive, so the sign stays.

The answer is x>−6.

Where students go wrong

Flipping the sign whenever a negative appears anywhere. It only flips when you multiply or divide the whole inequality by a negative, not when a negative number simply turns up in the working.

Also called inequality variable both sides or solving inequalities both sides.

Questions about these worksheets

Yes. Every inequalities with variables on both sides 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 inequalities with variables on both sides 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.

Flipping the sign whenever a negative appears anywhere. It only flips when you multiply or divide the whole inequality by a negative, not when a negative number simply turns up in the working.