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Real-World Inequalities Practice

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Real-World Inequalities Practice worksheet preview

Real-World Inequalities Practice

Mathematical inequalities illustration

📚 Part 1: Formulating Inequalities

1. Budget Constraint: Sarah has $120 to spend on concert tickets. Each ticket costs $18. Write an inequality to represent how many tickets (t) she can buy.
2. Travel Time: A delivery truck must complete its route in no more than 8 hours. If it takes 45 minutes to load and each delivery takes 25 minutes, write an inequality for the maximum number of deliveries (d).
3. Packing Weight: An airline allows a maximum baggage weight of 23 kg. Jake's suitcase weighs 3.5 kg empty. Write an inequality for the weight of items (w) he can pack.
4. Mobile Phone Plan: A phone plan costs $25 per month plus $0.50 per GB of data used. If Emma's budget is at most $45 per month, write an inequality for the data (g) she can use.

✏️ Part 2: Solving and Graphing

5. Solve the inequality from Question 1 and graph the solution on the number line below:

Number line: 0____1____2____3____4____5____6____7____8____9____10

6. A taxi charges $4.50 plus $2.20 per kilometre. If you have $35, solve the inequality 4.50 + 2.20k ≤ 35 to find the maximum distance you can travel.
7. Temperature Control: A greenhouse must maintain a temperature between 18°C and 26°C. Write a compound inequality and graph the acceptable temperature range.

Number line: 10____15____20____25____30____35°C

🌟 Part 3: Extension Challenge

8. Event Planning: A school is organising a fundraising dinner. The venue costs $300 to hire, and each meal costs $12. They want to raise at least $800 profit. If tickets are sold for $25 each, write and solve a compound inequality to find the range of tickets they need to sell.
9. Real-World Application: Create your own real-world scenario that involves an inequality. Write the problem, formulate the inequality, solve it, and explain what the solution means in context.

Success Criteria Check:

I can translate real-world problems into inequalities

I can solve linear inequalities using algebra

I can graph solutions on number lines correctly

I can explain my reasoning clearly

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