Linear Inequality Word Problems and Graphing with Two Variables

Claire’s stamp collection has 100 stamps and she buys 5 new stamps each month. Harriet’s collection has 400 stamps and she sells 15 stamps per month. Which inequality below could be used to determine after how many months Claire will have more stamps than Harriet?

• 100 - 5x > 400 + 15x

• 100 + 5x > 400 - 15x

• 100 + 5x < 400 - 15x

Claire’s stamp collection has 100 stamps and she buys 5 new stamps each month. Harriet’s collection has 400 stamps and she sells 15 stamps per month. After how many months will Claire have more stamps than Harriet?

• x < 15

• x > 15

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. Which inequality below could be used to determine when the blue roll will have more tickets than the pink roll?

• 1000 - 50x < 595 + 5x

• 1000 - 50x > 595 - 5x

• 1000 - 50x < 595 - 5x

• 1000x - 50 < 595 + 5x

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: 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

Store A charges $10 plus $0.25 per letter for engraving. Store B charges $16 plus $0.15 per letter. When will Store B cost less than Store A?

• x > 1.2

• x < 60

• x > 60

• x < 1.2

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 solution represents how many signatures Jo needs each week?