MathsFreePrintable

Real-World Inequalities Worksheet

A free maths worksheet ready for your classroom. Open in Kuraplan to grab the print-ready PDF, customize it for your students, or generate a fresh version in seconds.

Download now

Name:Date:

Real-World Inequalities Worksheet

Show your working for written problems. Include units where they are needed.

Inequality essentials

1.Which symbol means “at least”?

2.Solve the inequality 3x − 4 > 11.

x > 5
x < 5
x > 15
x < 15

3.A streaming service charges $12 per month, plus $1.50 for each rented film. Bodhi can spend no more than $30 this month. If f is the number of films she rents, which inequality models her spending?

12 + 1.5f ≤ 30
12 + 1.5f ≥ 30
1.5f ≤ 30
12f + 1.5 ≤ 30

Inequalities in context

4.A rideshare trip has a $5 starting fee and costs $1.80 per kilometre. Mei has $23 available. Let d be the distance in kilometres. Write and solve an inequality to find the greatest distance Mei can travel.

5.A community group needs at least $960 for new equipment. It has already collected $420 and will earn $6 for each raffle ticket sold. Let n be the number of tickets. Write and solve an inequality to find the fewest tickets needed.

6.A hiking track is open when the air temperature is from 12°C up to and including 24°C. Use t for the temperature and write a compound inequality for the safe range.

Show solutions on number lines

7.On the number line, mark the solution to x < 3. Use an open or closed endpoint as appropriate and show the direction of all solutions.

8.Use a number line to represent the rideshare solution from the earlier problem. Then state what the endpoint and shaded values mean for Mei’s trip.

9.A fitness centre charges a $90 joining fee and $38 per month. Kai wants to spend between $280 and $430, inclusive, on the joining fee and membership payments. Let m be the number of whole months. Write and solve a compound inequality, then give the possible whole-number values of m.