Inequality Graphs and Word Problems

James weighs 220 pounds and gains 2 pounds per month. Joey weighs 176 pounds and gains 4 pounds per month. Which inequality below could be used to determine after how many months James will weigh less than Joey?

• 220 + 2x > 176 + 4x

• 220 + 2x < 176 + 4x

James weighs 220 pounds and gains 2 pounds per month. Joey weighs 176 pounds and gains 4 pounds per month. After how many months will James weigh less than Joey?

• x < 22

• x > 22

Max’s dog dish contains 34 ounces of water, and Max drinks 4 ounces per hour. Sophie’s dog dish contains 50 ounces of water and she drinks 6 ounces per hour. Which inequality below can be used to determine after how many hours Sophie's dish will have less water than Max's dish?

• 34 - 4x > 50 - 6x

• 34 - 4x < 50 - 6x

Max’s dog dish contains 34 ounces of water, and Max drinks 4 ounces per hour. Sophie’s dog dish contains 50 ounces of water and she drinks 6 ounces per hour. In how many hours will Sophie’s dish have less water than Max’s?

• x > 8

• x < 8

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: 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