Real-World Inequalities Worksheet

Name:

Date:

Mathematical inequalities and real-world applications

📚 Part 1: Daily Review - Inequality Basics

1. Which symbol means "greater than or equal to"?

≤

≥

2. Solve: x + 5 ≤ 12

x ≤ 7

x ≤ 17

x ≥ 7

x ≥ 17

3. A mobile phone plan costs $25 per month plus $0.50 per text message. If Sarah wants to spend no more than $40 per month, which inequality represents this situation? (Let t = number of text messages)

25 + 0.5t ≤ 40

25 + 0.5t ≥ 40

25 + 0.5t < 40

0.5t ≤ 40

🚗 Part 2: Real-World Problem Solving

4. Taxi Fare Problem: A taxi charges $4.50 plus $2.20 per kilometre. If you have $25 to spend, write and solve an inequality to find the maximum distance you can travel.

a) Write the inequality: ________________

b) Solve algebraically:

c) Maximum distance: _______ kilometres

5. School Fundraiser: The Year 10 class needs to raise at least $800 for their excursion. They sell chocolates for $3 each and have already raised $350. How many chocolates do they need to sell?

a) Write the inequality: ________________

b) Solve:

c) Minimum chocolates needed: _______ chocolates

6. Temperature Range: The temperature in Perth today will be at least 18°C but no more than 28°C. Write this as a compound inequality using t for temperature.

Compound inequality: ________________

📊 Part 3: Graphing Solutions

7. Graph the solution to x ≥ -2 on the number line below:

8. For the taxi problem in Question 4, graph your solution on the number line and explain what it means in real life:

Real-world meaning:

9. Extension Challenge: A gym membership costs $45 per month plus a $120 joining fee. If someone budgets between $300 and $500 for their first year, write and solve a compound inequality to find the possible number of months they can afford.

Compound inequality: ________________

Solution work:

Range of months: ________________