Worksheets · Algebra 1

Inequality word problems worksheet for Algebra 1

Algebra 1 inequality word problems need a two-step inequality written from the words, solved, then read back in context. The answer is usually a whole number, so decide whether the situation calls for rounding up or down, and say what the number means.

Also taught in Pre-Algebra, 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 gift card has $35 on it. Each coffee costs $3.75. Eli wants to keep at least $6 on the card. How many coffees can Eli buy?
  2. A drone starts a flight with a full battery, 100 percent. The charge drops 6 percent each minute it flies. For how many whole minutes can it fly and land with at least 25 percent left?
  3. A shipping box may weigh at most 50 pounds. The empty box weighs 5 pounds, and each book weighs 2 pounds. How many books can be packed in the box?
  4. A boat has 11 gallons of fuel and uses 2.5 gallons an hour. The captain wants at least 2 gallons left at the end. How many whole hours can the boat run?
  5. A rowboat can hold at most 800 pounds. The two campers in it weigh 300 pounds together, and each bag of gear weighs 19 pounds. How many bags can they bring?
  6. A photo kiosk charges $2 to start an order plus $0.65 for each print. Lena can spend at most $20. How many prints can she order?
  7. A taco stand starts lunch with 260 tacos and sells about 16 tacos an hour. It must keep at least 45 tacos for the dinner rush. For how many whole hours can it sell at that rate?
  8. A canoe rental costs $10 plus $15 an hour. Kai cannot spend more than $60. For how many whole hours can Kai rent the canoe?
  9. A party hall costs $325 to rent plus $24 per guest. The budget is no more than $1150. How many guests can come?
  10. A phone plan costs $30 a month plus $8 for each gigabyte of data. Ava wants her bill to be at most $95. How many whole gigabytes can she use?

  1. Reach a goal: write, solve and round

    A reading challenge asks for at least 400 pages. Omar has read 116 pages and reads 26 pages a day. How many more days must he read?
  2. Each cup of lemonade sells for $1 and costs $0.35 to make. The stand cost $20 to set up. How many cups must be sold to make a profit of at least $25?
  3. Noah has $86 and saves $12 a week. How many weeks will it take him to have at least $310?
  4. A plane at 3500 feet climbs 650 feet a minute. After how many whole minutes will it be at 20000 feet or higher?
  5. Theo gets $10 a week for chores and $22 for each lawn he mows. How many lawns must he mow in a week to earn at least $190?
  6. A recycling center pays $0.65 for each pound of cans. How many whole pounds of cans must a class bring in to earn at least $75?
  7. A pool needs at least 11000 gallons of water. It has 3600 gallons, and a pump adds 33 gallons a minute. How many whole minutes must the pump run?
  8. A band paid $525 to have shirts printed and sells each shirt for $19. How many shirts must it sell to take in at least the $525 it paid?
  9. A club makes $2.25 profit on each box of cookies it sells. It has already raised $200. How many more boxes must it sell to raise at least $400 in all?
  10. A basketball player has scored 79 points this season and scores about 23 points a game. How many more games until she has at least 300 points?

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

Sigma Prep · sigmaprep.io/worksheets

Name

Inequality Word ProblemsAnswer keyVersion 2

Date Period

Write and solve an inequality for each problem.

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

    A gift card has $35 on it. Each coffee costs $3.75. Eli wants to keep at least $6 on the card. How many coffees can Eli buy?35−3.75c≥6; c≤71115, so at most 7 coffees
  2. A drone starts a flight with a full battery, 100 percent. The charge drops 6 percent each minute it flies. For how many whole minutes can it fly and land with at least 25 percent left?100−6m≥25; m≤12.5, so at most 12 minutes
  3. A shipping box may weigh at most 50 pounds. The empty box weighs 5 pounds, and each book weighs 2 pounds. How many books can be packed in the box?5+2b≤50; b≤22.5, so at most 22 books
  4. A boat has 11 gallons of fuel and uses 2.5 gallons an hour. The captain wants at least 2 gallons left at the end. How many whole hours can the boat run?11−2.5h≥2; h≤3.6, so at most 3 hours
  5. A rowboat can hold at most 800 pounds. The two campers in it weigh 300 pounds together, and each bag of gear weighs 19 pounds. How many bags can they bring?300+19b≤800; b≤26619, so at most 26 bags
  6. A photo kiosk charges $2 to start an order plus $0.65 for each print. Lena can spend at most $20. How many prints can she order?2+0.65p≤20; p≤27913, so at most 27 prints
  7. A taco stand starts lunch with 260 tacos and sells about 16 tacos an hour. It must keep at least 45 tacos for the dinner rush. For how many whole hours can it sell at that rate?260−16h≥45; h≤13716, so at most 13 hours
  8. A canoe rental costs $10 plus $15 an hour. Kai cannot spend more than $60. For how many whole hours can Kai rent the canoe?10+15h≤60; h≤313, so at most 3 hours
  9. A party hall costs $325 to rent plus $24 per guest. The budget is no more than $1150. How many guests can come?325+24g≤1150; g≤3438, so at most 34 guests
  10. A phone plan costs $30 a month plus $8 for each gigabyte of data. Ava wants her bill to be at most $95. How many whole gigabytes can she use?30+8g≤95; g≤818, so at most 8 gigabytes

  1. Reach a goal: write, solve and round

    A reading challenge asks for at least 400 pages. Omar has read 116 pages and reads 26 pages a day. How many more days must he read?116+26d≥400; d≥101213, so at least 11 days
  2. Each cup of lemonade sells for $1 and costs $0.35 to make. The stand cost $20 to set up. How many cups must be sold to make a profit of at least $25?0.65c−20≥25; c≥69313, so at least 70 cups
  3. Noah has $86 and saves $12 a week. How many weeks will it take him to have at least $310?86+12w≥310; w≥1823, so at least 19 weeks
  4. A plane at 3500 feet climbs 650 feet a minute. After how many whole minutes will it be at 20000 feet or higher?3500+650m≥20000; m≥25513, so at least 26 minutes
  5. Theo gets $10 a week for chores and $22 for each lawn he mows. How many lawns must he mow in a week to earn at least $190?10+22l≥190; l≥8211, so at least 9 lawns
  6. A recycling center pays $0.65 for each pound of cans. How many whole pounds of cans must a class bring in to earn at least $75?0.65p≥75; p≥115513, so at least 116 pounds
  7. A pool needs at least 11000 gallons of water. It has 3600 gallons, and a pump adds 33 gallons a minute. How many whole minutes must the pump run?3600+33m≥11000; m≥224833, so at least 225 minutes
  8. A band paid $525 to have shirts printed and sells each shirt for $19. How many shirts must it sell to take in at least the $525 it paid?19s≥525; s≥271219, so at least 28 shirts
  9. A club makes $2.25 profit on each box of cookies it sells. It has already raised $200. How many more boxes must it sell to raise at least $400 in all?200+2.25b≥400; b≥8889, so at least 89 boxes
  10. A basketball player has scored 79 points this season and scores about 23 points a game. How many more games until she has at least 300 points?79+23g≥300; g≥91423, so at least 10 games

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

How to do these

You have $50. A fair charges $5 to enter and $3 per ride. What is the greatest number of rides you can take?

  1. Entry plus rides must be at most 50: 5 + 3r ≤ 50.
  2. Subtract 5 and divide by 3: r ≤ 15, and rides come whole, so 15.

The answer is 15.

Where students go wrong

Using < or > when the words say at least or at most. At least $299 includes exactly $299, so the inequality is ≥ and the boundary value counts.

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.

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 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.