Worksheets · Algebra 2

Algebra 2 compound inequalities worksheet

Two inequalities at once. The "and" kind is squeezed between two numbers and every step happens to all three parts; the "or" kind is two separate problems whose answers are joined.

Select your difficulty

Pick more than one for a sheet that mixes them.

The preview can look cramped on a phone. The PDF and printed sheet come out normal.

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

Sigma Prep · sigmaprep.io/worksheets

Name

Compound Inequalities

Date Period

Solve each inequality.

  1. −71≤−6a+7<−17
  2. −5y−2>18 or −3y−12<−18
  3. −23≤−7x+12<−2
  4. 10n−5<−15 or −8n−4≤−44
  5. 23<−4v+11≤47
  6. 10p+15≤−45 or 10p−1>19
  7. −15≤10k−15≤5
  8. −4n+2>22 or 6n+13>1
  9. −31≤4m−3<−7
  10. 3x−12≤−30 or 6x−15≥−3
  11. −18≤−2x−4≤−12
  12. −2k+5≥5 or −5k+5≤−40
  13. −1<4a+15<11
  14. −9n−13≥41 or −4n−14<2
  15. −30<−4a−10≤−2
  16. −9a−10≥71 or 5a−14≥−39
  17. −3<−2a+5≤1
  18. −3v+6>0 or 2v+4≥12
  19. 25≤−9y−11≤61
  20. 6n+4≤−32 or −3n−10<−22

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

Sigma Prep · sigmaprep.io/worksheets

Name

Compound InequalitiesAnswer keyVersion 1

Date Period

Solve each inequality.

  1. −71≤−6a+7<−174<a≤13
  2. −5y−2>18 or −3y−12<−18y<−4 or y>2
  3. −23≤−7x+12<−22<x≤5
  4. 10n−5<−15 or −8n−4≤−44n<−1 or n≥5
  5. 23<−4v+11≤47−9≤v<−3
  6. 10p+15≤−45 or 10p−1>19p≤−6 or p>2
  7. −15≤10k−15≤50≤k≤2
  8. −4n+2>22 or 6n+13>1n<−5 or n>−2
  9. −31≤4m−3<−7−7≤m<−1
  10. 3x−12≤−30 or 6x−15≥−3x≤−6 or x≥2
  11. −18≤−2x−4≤−124≤x≤7
  12. −2k+5≥5 or −5k+5≤−40k≤0 or k≥9
  13. −1<4a+15<11−4<a<−1
  14. −9n−13≥41 or −4n−14<2n≤−6 or n>−4
  15. −30<−4a−10≤−2−2≤a<5
  16. −9a−10≥71 or 5a−14≥−39a≤−9 or a≥−5
  17. −3<−2a+5≤12≤a<4
  18. −3v+6>0 or 2v+4≥12v<2 or v≥4
  19. 25≤−9y−11≤61−8≤y≤−4
  20. 6n+4≤−32 or −3n−10<−22n≤−6 or n>4

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

How to do these

−2<3x+1≤7

  1. Subtract 1 from all three parts: -3 < 3x ≤ 6.
  2. Divide all three by 3.
  3. That leaves -1 < x ≤ 2.

The answer is −1<x≤2.

Where students go wrong

Doing the operation to only two of the three parts. Everything you do has to happen in all three places at once. On the "or" kind the mistake is different: the two halves are separate problems and the answers do not have to meet.

Also called "and" and "or" inequalities or conjunction and disjunction inequalities.

What you can put on this worksheet

Squeezed between two numbers
1<v+3<8 → −2<v<5
Two inequalities joined by "or"
v−5≤−8 or v+3>8 → v≤−3 or v>5
Mix in some with no solution
v−5≥0 and v+3<1 → No solution
Mix in some true for every number
v−5≤0 or v+3>1 → All real numbers
Two separate parts, fractions, letters on both sides, three parts
m4≥1 or m4<−4 → m<−16 or m≥4
A fraction in the middle, or in one part
n−5≥−5 and n6≤2 → 0≤n≤12

Questions about these worksheets

Yes. Every compound 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 2 is usually taken around 10th or 11th 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 compound 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 6: squeezed between two numbers, two inequalities joined by "or", mix in some with no solution, mix in some true for every number, two separate parts, fractions, letters on both sides, three parts and a fraction in the middle, or in one part. Tick as many as you want and set how many of each, or let it spread them evenly.

Doing the operation to only two of the three parts. Everything you do has to happen in all three places at once. On the "or" kind the mistake is different: the two halves are separate problems and the answers do not have to meet.