📊 Part 1: Solving Linear Inequalities

1. Solve the inequality: 3x + 2 > 8

Solution: x ______

2. Solve the inequality: -2x + 5 ≤ 11

Solution: x ______

3. Solve the inequality: 4x - 7 < 9

Solution: x ______

4. When solving -3x > 12, what happens to the inequality sign?

It stays the same

It flips direction

It becomes an equals sign

📈 Part 2: Graphing on Number Lines

5. Graph the solution x > 3 on the number line below. Use an open or closed circle as appropriate.

6. Graph the solution x ≤ -1 on the number line below.

7. Which symbol represents "greater than or equal to"?

>

≥

<

≤

8. When graphing x < 5, you should use:

An open circle at 5

A closed circle at 5

A square at 5

🔗 Part 3: Compound Inequalities

9. Solve and graph: x > 2 AND x ≤ 6

This means x is between _____ and _____ (including/excluding the endpoints as appropriate).

10. Solve and graph: x < 1 OR x ≥ 4

This represents two separate regions. Explain what values of x satisfy this compound inequality:

11. Real-world application: A movie theater offers discounted tickets for children under 12 years old OR seniors 65 years and older. Write this as a compound inequality using age (a) and graph the solution.

Compound inequality: _________________

12. Explain the difference between "AND" and "OR" in compound inequalities:

Linear Inequalities Graphing

Linear Inequalities Graphing

📊 Part 1: Solving Linear Inequalities

📈 Part 2: Graphing on Number Lines

🔗 Part 3: Compound Inequalities

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