Worksheets · Pre-Algebra

Inequality word problems worksheet for Pre-Algebra

"At most" means less than or equal to; "at least" means greater than or equal to. Solve as you would an equation, then round the right way: you cannot buy part of a ride, so a budget rounds down and a goal rounds up.

Also taught in Algebra 1, at its own level and with its own examples.

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

Inequality Word Problems

Date Period

Write and solve an inequality for each problem.

  1. Stay within a limit: write, solve and round

    A shipping box may weigh at most 70 pounds. The empty box weighs 3 pounds, and each book weighs 3 pounds. How many books can be packed in the box?
  2. A hiker's pack can weigh no more than 32 pounds. The pack and gear weigh 3 pounds, and each bottle of water weighs 2.5 pounds. How many bottles can the hiker carry?
  3. A party hall costs $350 to rent plus $13 per guest. The budget is no more than $750. How many guests can come?
  4. A gift card has $40 on it. Each coffee costs $4.50. Eli wants to keep at least $9 on the card. How many coffees can Eli buy?
  5. A rowboat can hold at most 700 pounds. The two campers in it weigh 330 pounds together, and each bag of gear weighs 20 pounds. How many bags can they bring?
  6. A taco stand starts lunch with 360 tacos and sells about 28 tacos an hour. It must keep at least 25 tacos for the dinner rush. For how many whole hours can it sell at that rate?
  7. A concert can last at most 120 minutes. The opening act takes 25 minutes, and each song the band plays takes 3 minutes. How many songs can the band play?
  8. A drone starts a flight with a full battery, 100 percent. The charge drops 12 percent each minute it flies. For how many whole minutes can it fly and land with at least 15 percent left?
  9. A boat has 16 gallons of fuel and uses 3.5 gallons an hour. The captain wants at least 1 gallon left at the end. How many whole hours can the boat run?
  10. A canoe rental costs $30 plus $10 an hour. Kai cannot spend more than $145. For how many whole hours can Kai rent the canoe?

  1. Reach a goal: write, solve and round

    A band paid $375 to have shirts printed and sells each shirt for $22. How many shirts must it sell to take in at least the $375 it paid?
  2. A basketball player has scored 95 points this season and scores about 21 points a game. How many more games until she has at least 250 points?
  3. Theo gets $20 a week for chores and $22 for each lawn he mows. How many lawns must he mow in a week to earn at least $100?
  4. A recycling center pays $0.45 for each pound of cans. How many whole pounds of cans must a class bring in to earn at least $25?
  5. A plane at 3500 feet climbs 1150 feet a minute. After how many whole minutes will it be at 13000 feet or higher?
  6. Noah has $81 and saves $10 a week. How many weeks will it take him to have at least $370?
  7. Each cup of lemonade sells for $1.25 and costs $0.30 to make. The stand cost $20 to set up. How many cups must be sold to make a profit of at least $20?
  8. A club makes $1.50 profit on each box of cookies it sells. It has already raised $90. How many more boxes must it sell to raise at least $700 in all?
  9. A pool needs at least 12000 gallons of water. It has 2600 gallons, and a pump adds 33 gallons a minute. How many whole minutes must the pump run?
  10. A reading challenge asks for at least 300 pages. Omar has read 116 pages and reads 30 pages a day. How many more days must he read?

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

Sigma Prep · sigmaprep.io/worksheets

Name

Inequality Word ProblemsAnswer keyVersion 1

Date Period

Write and solve an inequality for each problem.

  1. Stay within a limit: write, solve and round

    A shipping box may weigh at most 70 pounds. The empty box weighs 3 pounds, and each book weighs 3 pounds. How many books can be packed in the box?3+3b≤70; b≤2213, so at most 22 books
  2. A hiker's pack can weigh no more than 32 pounds. The pack and gear weigh 3 pounds, and each bottle of water weighs 2.5 pounds. How many bottles can the hiker carry?3+2.5w≤32; w≤11.6, so at most 11 bottles
  3. A party hall costs $350 to rent plus $13 per guest. The budget is no more than $750. How many guests can come?350+13g≤750; g≤301013, so at most 30 guests
  4. A gift card has $40 on it. Each coffee costs $4.50. Eli wants to keep at least $9 on the card. How many coffees can Eli buy?40−4.5c≥9; c≤689, so at most 6 coffees
  5. A rowboat can hold at most 700 pounds. The two campers in it weigh 330 pounds together, and each bag of gear weighs 20 pounds. How many bags can they bring?330+20b≤700; b≤18.5, so at most 18 bags
  6. A taco stand starts lunch with 360 tacos and sells about 28 tacos an hour. It must keep at least 25 tacos for the dinner rush. For how many whole hours can it sell at that rate?360−28h≥25; h≤112728, so at most 11 hours
  7. A concert can last at most 120 minutes. The opening act takes 25 minutes, and each song the band plays takes 3 minutes. How many songs can the band play?25+3s≤120; s≤3123, so at most 31 songs
  8. A drone starts a flight with a full battery, 100 percent. The charge drops 12 percent each minute it flies. For how many whole minutes can it fly and land with at least 15 percent left?100−12m≥15; m≤7112, so at most 7 minutes
  9. A boat has 16 gallons of fuel and uses 3.5 gallons an hour. The captain wants at least 1 gallon left at the end. How many whole hours can the boat run?16−3.5h≥1; h≤427, so at most 4 hours
  10. A canoe rental costs $30 plus $10 an hour. Kai cannot spend more than $145. For how many whole hours can Kai rent the canoe?30+10h≤145; h≤11.5, so at most 11 hours

  1. Reach a goal: write, solve and round

    A band paid $375 to have shirts printed and sells each shirt for $22. How many shirts must it sell to take in at least the $375 it paid?22s≥375; s≥17122, so at least 18 shirts
  2. A basketball player has scored 95 points this season and scores about 21 points a game. How many more games until she has at least 250 points?95+21g≥250; g≥7821, so at least 8 games
  3. Theo gets $20 a week for chores and $22 for each lawn he mows. How many lawns must he mow in a week to earn at least $100?20+22l≥100; l≥3711, so at least 4 lawns
  4. A recycling center pays $0.45 for each pound of cans. How many whole pounds of cans must a class bring in to earn at least $25?0.45p≥25; p≥5559, so at least 56 pounds
  5. A plane at 3500 feet climbs 1150 feet a minute. After how many whole minutes will it be at 13000 feet or higher?3500+1150m≥13000; m≥8623, so at least 9 minutes
  6. Noah has $81 and saves $10 a week. How many weeks will it take him to have at least $370?81+10w≥370; w≥28.9, so at least 29 weeks
  7. Each cup of lemonade sells for $1.25 and costs $0.30 to make. The stand cost $20 to set up. How many cups must be sold to make a profit of at least $20?0.95c−20≥20; c≥42219, so at least 43 cups
  8. A club makes $1.50 profit on each box of cookies it sells. It has already raised $90. How many more boxes must it sell to raise at least $700 in all?90+1.5b≥700; b≥40623, so at least 407 boxes
  9. A pool needs at least 12000 gallons of water. It has 2600 gallons, and a pump adds 33 gallons a minute. How many whole minutes must the pump run?2600+33m≥12000; m≥2842833, so at least 285 minutes
  10. A reading challenge asks for at least 300 pages. Omar has read 116 pages and reads 30 pages a day. How many more days must he read?116+30d≥300; d≥6215, so at least 7 days

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

How to do these

You have $50. Entry is $8 and each ride is $6. The most rides?

  1. 8 + 6r ≤ 50, so 6r ≤ 42 and r ≤ 7.

The answer is 7.

Where students go wrong

Rounding the wrong way. If the inequality gives 5.3 weeks to reach a goal, 5 weeks is not enough: the answer is 6.

Also called writing inequalities or inequality applications.

What you can put on this worksheet

One step, limits, and two plans compared
Movie tickets cost $12 each. You can spend at most $96. How many tickets can you buy? → 12t≤96; t≤8, so at most 8 tickets
Two steps, goals, averages, percents and ranges
A garage charges $6 for the first hour and $4 for each extra hour. Dev has $14. How many extra hours can Dev park? → 6+4h≤14; h≤2, so at most 2 extra hours

Questions about these worksheets

Yes. Every inequality word problems 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 inequality word problems 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 2: one step, limits, and two plans compared and two steps, goals, averages, percents and ranges. Tick as many as you want and set how many of each, or let it spread them evenly.

Rounding the wrong way. If the inequality gives 5.3 weeks to reach a goal, 5 weeks is not enough: the answer is 6.