Inequalities Word Problems

Four times a number increased by  7 is at least 19. 

• 4x > 19
• 4x + 7 ≥ 19
• 4x < 19
• 4x + 7 ≤ 19

Translate into an inequality:
2 times a number is greater than 6

• 2-x<6
• 2x>6
• 2x>-6
• 2x<6

at least

• <
• >
• ≤
• ≥

The dance committee hired a DJ for the fall dance. The DJ charges $125 per hour in addition to $55 for an assistant. The committee wants to keep the total cost under $600. Which inequality represents the maximum amount of hours the DJ will play at the dance?

• 125x + 55 ≤ 600
• 125x + 55 ≥ 600
• 125x + 55 > 600
• 125x + 55 < 600

A willow tree is 5.1 feet tall and grows at a rate of 2.5 feet a year. After how many years will the tree have reached no more than 60 feet tall?

• 5.1 + 2.5y ≥ 60
• 60 < 5.1 + 2.5
• 5.1 + 2.5y ≤ 60
• 5.1 + 2.5y > 60

Which is an algebraic expression for "six less than k".

• 6/k
• k/6
• 6 - k
• k - 6

Mrs. Scott decided that she would spend no more than $120 to buy a jacket and a skirt. If the price of the jacket was $20 more than 3 times the price of the skirt, which inequality represents the highest possible price of the skirt?

• 20x + 120 ≥ 3
• x/3 + 20 ≤ 120
• 3x + 20 ≤ 120
• 3x + 20 ≥ 120

Oak Park had more than 450 students win a Zaxby's sandwich. Let s represent the number of students who won a sandwich.

• s > 450

• s < 450

• s ≤ 450

• s ≥ 450

• s = 450

The movie will be 90 minutes or longer. Let m represent the length of the movie.

• m > 90

• m < 90

• m ≤ 90

• m ≥ 90

• m = 90

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