Justifying Inequality Solutions

Name:

Date:

Student presenting mathematical solution

📚 Part 1: Daily Review - Inequality Basics

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

≥

≤

2. When graphing x ≤ 3 on a number line, you would use:

An open circle at 3

A closed circle at 3

An arrow pointing right only

No circle at all

3. Check all methods you can use to verify an inequality solution:

Substitution

Test points

Graphical interpretation

Guessing

✏️ Part 2: Written Justification Practice

4. Maya solved the inequality 2x + 5 ≤ 15 and got x ≤ 5. Write a complete justification for her solution including verification.

5. A cinema charges $12 per ticket. Sarah has $50 to spend. The inequality 12t ≤ 50 represents this situation where t is the number of tickets. Explain why t ≤ 4.17 means Sarah can buy a maximum of _____ tickets.

6. Complete this justification: "To verify x = 3 is a solution to 2x - 1 ≥ 5, I substitute: 2(3) - 1 = _____, and since _____ ≥ 5 is _______, x = 3 is a valid solution."

🎯 Part 3: Real-Life Justification

7. Tom wants to buy notebooks that cost $3 each. He has $20 and needs to keep at least $5 for lunch. Write and justify the inequality that represents this situation.

8. Reflection: Why is it important to justify mathematical solutions in real-life situations? Give one specific example.

9. Extension Challenge: Create your own real-life inequality problem involving temperature in Celsius, then solve and justify your solution.