Inequality Algebra

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

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

Work this one out on paper.

Solve.

-138 ≥ -6 (6b − 7)

• b ≤ 5

• b ≤ -5

• b ≥ 5

• b ≥ -5

Solve:
-8(x - 3) - 4x < 108

• x > -38

• x > -14

• x > -7

• x < -38

A limo driver needs to make more than $450 in one day. He charges a rental fee of $375 plus $0.85 per mile. What inequality represents the number of miles, x, he would have to drive to reach his goal?

• 0.85x + 375 > 450

• 0.85x + 375 < 450

• 0.85 + 375x > 450

• 0.85 + 375x < 450

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

Solve.

• x is greater than -28

• x is greater than 28

• x is greater than -14

• x is greater than 14

Emilia needs at least $240 to buy new headphones. She has already saved $30. She earns $14 per car that she washes. What is the least number of cars she can wash to buy the headphones? Solve the inequality/answer the question.

• x ≥ 15

• x ≤ 15

• x > 15

• x < 15

Which is the solution of
-4 - 6m > -9m + 8?

• m < -4

• m > 4

• m < 15

• m > 36

Annie wants to spend at most $12.50 on school supplies. She needs to purchase a binder (cost $7.00) and wants to spend the rest on pens, which cost $0.75 each. Which inequality represents this situation, where x is the number of pens Annie can buy?