Inequalities Worded Problems

After addressing 75 envelopes, a political volunteer has fewer than 26 envelopes left to address.  Which inequality can be used to find the total number of envelopes (e)?

• 75 - e < 26
• e - 75 < 26
• 75 - e > 26
• e - 75 > 26

Clark and John cut the grass of a neighbor's lawn.  Clark started the job and then John finished the job, working 1/2 hour longer than Clark.  The job took at least 2 hours.  Which inequality can be used to find the number of hours Clark worked (c)?

• c + (c + 0.5) ≥ 2
• c + (c + 0.5) ≤ 2
• c + (c - 0.5) ≥ 2
• c + (c - 0.5) ≤ 2

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 and your friend are planning to walk across an old bridge. The bridge can hold at most 1000 pounds. The total weight of the people currently on the bridge is 675 pounds. You weigh 156 pounds.Write and solve an inequality that represents how much your friend can weigh within the limits of the bridge.

• X ≤ 169 
• X < 169
• X < 156
• X > 156 

You order a new pair of running shoes from a website that offers free shipping on orders of $75 or more. Your shoes cost $69.95. Write and solve an inequality that represents how much more you must spend to get free shipping. 

• X > 5.05
• X ≥ 5. 05
• X > 69.95
• X ≥ 69.95

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

Solve the following inequality:
-4x + 14 ≤ 54

• x ≥ -10
• x ≤ -10
• x ≥ 10
• x ≤ 10