Worksheets · Algebra 1

Multi-step inequalities worksheet for Algebra 1

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. A couple of questions on each level are word problems to set up and answer in context.

Also taught in Pre-Algebra and Algebra 2, each at its own level and with its own examples.

Not quite the one you need? Same words, different skill:

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Pick more than one for a sheet that mixes them.

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

Sigma Prep · sigmaprep.io/worksheets

Name

Multi-Step Inequalities

Date Period

Solve each inequality, or answer the question.

  1. Combine like terms, then solve

    4a+11a−30<270
  2. 3p−6p−14≥−29
  3. −10k+2k+15≤−105
  4. −6y−3y−29≥−155
  5. −5p+13p−26<−178

  1. Solve with the variable on both sides

    −3p−26>−p−8
  2. −9r+25≤4r+103
  3. 8m+28<2m−14
  4. −11y−27<−4y−13
  5. −9k−18≤−8k−16

  1. Distribute, then solve

    7(b−9)<−126
  2. 7(p+12)>224
  3. −6(b+11)<42
  4. 6(m−11)≥−12
  5. 7(v−12)>−203

  1. Solve inequality word problems

    Your first 3 test scores are 87, 76 and 86. What is the least score on the next test that makes your mean at least 85?
  2. You have $36. A fair charges $3 to enter and $3 per ride. What is the greatest number of rides you can take?
  3. A tank holds 406 gallons and drains 13 gallons a minute. For at most how many whole minutes can it drain and still hold at least 181 gallons?
  4. Your first 3 test scores are 72, 74 and 82. What is the least score on the next test that makes your mean at least 78?
  5. A tank holds 445 gallons and drains 20 gallons a minute. For at most how many whole minutes can it drain and still hold at least 251 gallons?

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, or answer the question.

  1. Combine like terms, then solve

    4a+11a−30<270a<20
  2. 3p−6p−14≥−29p≤5
  3. −10k+2k+15≤−105k≥15
  4. −6y−3y−29≥−155y≤14
  5. −5p+13p−26<−178p<−19

  1. Solve with the variable on both sides

    −3p−26>−p−8p<−9
  2. −9r+25≤4r+103r≥−6
  3. 8m+28<2m−14m<−7
  4. −11y−27<−4y−13y>−2
  5. −9k−18≤−8k−16k≥−2

  1. Distribute, then solve

    7(b−9)<−126b<−9
  2. 7(p+12)>224p>20
  3. −6(b+11)<42b>−18
  4. 6(m−11)≥−12m≥9
  5. 7(v−12)>−203v>−17

  1. Solve inequality word problems

    Your first 3 test scores are 87, 76 and 86. What is the least score on the next test that makes your mean at least 85?87+76+86+x4≥85; 91 points
  2. You have $36. A fair charges $3 to enter and $3 per ride. What is the greatest number of rides you can take?3+3r≤36; 11 rides
  3. A tank holds 406 gallons and drains 13 gallons a minute. For at most how many whole minutes can it drain and still hold at least 181 gallons?406−13m≥181; 17 minutes
  4. Your first 3 test scores are 72, 74 and 82. What is the least score on the next test that makes your mean at least 78?72+74+82+x4≥78; 84 points
  5. A tank holds 445 gallons and drains 20 gallons a minute. For at most how many whole minutes can it drain and still hold at least 251 gallons?445−20m≥251; 9 minutes

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 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
Mix in some with no solution
(v+2)≤v−2 → No solution
Mix in some true for every number
(v+2)≤v+6 → All real numbers
The variable on the right
7≥3v+4v → v≤1
Parentheses, then the variable on both sides
3(4v+4)≤4(v+5) → v≤1
Inequality word problems
You have saved $121 and save $20 a week. How many weeks until you have at least $211? → 121+20w≥211; 5 weeks
Write one with a given solution
Write an inequality with n on both sides whose solution is n>1 → e.g. 17−5n<3n+9

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.

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 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 9: like terms to collect, the variable on both sides, parentheses to expand, mix in some with no solution, mix in some true for every number, the variable on the right, parentheses, then the variable on both sides, inequality word problems and write one with a given solution. 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.