Writing and Solving Inequalities

"4 more than triple a number is less than 82"

• 3x + 4 < 82

• 3x + 4 > 82

• 82 - 3x + 4

• 3x + 4 < 82

Aaron is planning a trip.  He found a flight for $130 and a hotel that charges $96 a night.  Aaron wants to spend no more than $850 on hotel and airfare.  Write an inequality Aaron can use to determine how many nights he can stay.

Three times the difference of a number and five is under nine times the number increased by three.

The Starlight Bowling Alley charges $6 to rent shoes and $8 per game (g). Cameron has only $42 to spend. Which inequality represents this scenario if “g” represents the number of games Cameron can play?

• 6g + 8 ≥ 42

• 8g + 6 ≤ 42

• 6g + 8 > 42

• 8g + 6 < 42

The Starlight Bowling Alley charges $6 to rent shoes and $8 per game. Cameron has only $42 to spend. Which inequality represents this scenario if “x” represents the number of games Cameron can play?

• 6x + 8 ≥ 42

• 8x + 6 ≤ 42

• 6x + 8 > 42

• 8x + 6 < 42

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

Cody’s Gym charges a $15 fee to join and $30 per month. Tyler’s Gym charges a $30 fee to join and $20 per month. Write an inequality that could be used to determine after how many months Tyler’s gym would be a better deal.

• 30 + 20x < 15 + 30x

• 30x + 20 < 15x + 30

• 30 + 20x > 15 + 30x

• 30x + 20 > 15x + 30

You want to save at least $250. You currently have $50 and you babysit for $15. How many hours should you babysit in order to meet your goal?

• 13 hours or less

• 13 hours or more

• 14 hours or less

• 14 hours or more

Mark's Canoes rents canoes for a $20 fee plus $35 per hour. You do not want to spend more than $150. For how many hours can you afford to rent the canoe?

• 3 hours maximum

• 3 hours minimum

• 4 hours maximum

• 4 hours minimum