Linear Inequality Word Problems

A pink roll of tickets has 1,000 tickets on it, and 50 are sold each hour. A blue roll has 595 tickets, and 5 are sold each hour. When will the blue roll have more tickets than the pink roll?

• x > 9

• x < 9

Which inequality represents:

3 less than twice a number is at least the number plus 5

Which inequality represents:Twice the sum of a number and 2 is fewer than three times the same number minus 8

Which inequality represents:

5 times a number is not less than twice the number plus 9

Lea needs at least $240 to buy new headphones. She has already saved $30. She earns $14 per car that she washes. Which inequality below can be used to determine how many cars she has to wash to have enough money?

• 14x+30 ≥ 240

• 14x+30 ≤ 240

• 30x+14 ≥ 240

• 30x+14 ≤ 240

Sam earns a weekly salary of $300. He also earns a commission of 4% on all of his sales. Which inequality below can be used to determine dollar amount of sales he must make to have a total weekly pay of at least $550?

• 0.04x+300 ≥ 550

• 0.04x+300≤ 550

• 4x+300 ≥ 550

• 4x+300 ≤ 550

Todd caught at least three times as many fish this year than last year. He caught 63 fish this year. Which inequality represents how many fish he caught last year? 

• 3y > 63

• 3y < 63

• 3y ≤ 63

• 3y ≥ 63

Write an inequality:
Twenty-two more than four times a number is less than 82.

• 22 + 4n ≤ 82

• 22 + 4n > 82

• 82 + 22n ≥ 4

• 22 + 4n < 82

The speed limit is 45. Katie was going thirty miles per hour and sped up some. Which inequality represents the amount she could speed up and not be speeding?

• 30 + s ≥ 45

• 30 - s ≥ 45

• 30 + s ≤ 45

• 30 - s ≤ 45

Jo needs to collect at least 1,000 signatures for a petition. He has 520 and wants to collect the same number each week. He has 6 more weeks. Which inequality represents this situation?