Linear Inequality Problems

Allison practices her violin for at least 12 hours per week. She practices for three fourths of an hour each session. If Allison has already practiced 3 hours this week, how many more sessions remain for her to meet or exceed her weekly practice goal?

• 3/4h + 3 > 12

• 3/4h + 3 ≥ 12

• 0.75h - 3 <12

• 0.75h - 3 ≤ 12

Pet Supplies makes a profit of $5.50 per bag on its line of natural dog food. If the store wants to make a profit of no less than $5225, how many bags of dog food does it need to sell?

• 5.50b < 5225

• 5.50b ≤ 5225

• 5.50b > 5225

• 5.50b ≥ 5225

Ryan is a wrestler trying to make weight. He currently weighs 200 lbs. If he cuts 2 lbs. per week, how many weeks will it take him to weigh less than 175 lbs.?

• 200 - 2w < 175

• 200 - 2w ≤ 175

• 175 - 2w < 200

• 175 - 2w ≤ 200

Tom is deciding whether or not he should become a member gym to use their basketball courts. The membership cost is $135. Members pay $2 to rent out the basketball courts. Non-members can rent the court also, but they have to pay $11 each time. how many times would Tom need to rent the court in order for it be cheaper to be a member than a non member?

• 135 + 2c > 11

• 135 + 2c < 11

• 135 + 2c > 11c

• 135 + 2c < 11c

Which of the following DOES NOT imply we should use a > symbol?

• More than

• At least

• At minimum

• At maximum

If the question says that we can have at most 15 people in the elevator, which option could end our equation?

• > 15

• < 15

• ≥ 15

• ≤ 15

Which of the following phrases DOES NOT imply that we should use a < symbol?

• No more than

• Less than

• At least

• Or less

Yellow Cab Taxi charges a $1.75 flat rate in addition to $0.65 per mile.  Katie has no more than $10 to spend on the taxi ride.

• 1.75 + 0.65m < 10

• 1.75 + 0.65m > 10

• 1.75m + 0.65 < 10

• 1.75m + 0.65 > 10

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

Which situation can be represented by the inequality
15 + 6x ≤ 100?

• Lazer Zone charges $15 plus $6 per person. If Andrea has a maximum of $100 to spend, how many people can Andrea invite to play laser tag?

• Lazer Zone charges $6 plus $15 per person. If Andrea has a maximum of $100 to spend, how many people can Andrea invite to play laser tag?

• Lazer Zone charges $15 plus $6 per person. If Andrea has a minimum of $100 to spend, how many people can Andrea invite to play laser tag?

• Lazer Zone charges $6 plus $15 per person. If Andrea has a minimum of $100 to spend, how many people can Andrea invite to play laser tag?