Inequalities Solving and Graphing

To qualify for an award, a student volunteers no less than 5 hours each week at the local hospital. Write an inequality that represents how many hours the student volunteers each week.

• X < 5

• X > 5

• X ≥ 5

• X ≤ 5

A student must be at least 15 years old to obtain a driver’s permit.

• x > 15

• x < 15

• x ≤ 15

• x ≥ 15

To order from the kids menu a person must be no more than 12 years old.

• x > 12

• x < 12

• x ≥ 12

• x ≤ 12

You bike for 2 hours at a speed no faster than 17.6 miles per hour. Write and solve an inequality that represents the possible numbers of miles you bike.

• X ≤ 17.6

• X ≥ 17.6

• X ≥ 35.2

• X ≤ 35.2

Which of the following inequalities would require you to flip the sign when solving?

• 2x < 3

• 3x > - 9

• -4x ≥ 10

• 5x ≤ 15

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

A limo driver needs to make more than $450 in one day. He charges a rental fee of $375 and $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

Write an inequality for the situation:

George rented a bike for 4 hours. There was a $10 dollar deposit to pay in addition to the hourly rate. What was the hourly rate if the total came to less than or equal to $65?

• 10x + 65 ≥ 40

• 4x + 10 ≤ 65

• 4x - 10 ≤ 65

• 65 + 4x ≥ 40

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

Solve the inequality (just like solving a 2 Step equation):

7b - 3 < 11

• b < 2

• 84 > b

• b > 2

• b < 84