1.6 Solving Linear Inequalities

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This document discusses how to solve and graph linear inequalities, including graphing one-variable inequalities, solving one-variable inequalities algebraically, and solving compound inequalities involving "and" or "or". Examples are provided for graphing and solving various linear inequalities and compound inequalities involving one variable.

1.6 Solving Linear Inequalities

Graphing One Variable Inequalities
• Graph x < 3

• Graph x ≥ -2

Solving 1-Variable Inequalities
• Solve 5y – 8 12

• Graph the solution.

• Solve 2x + 1 6x – 1

Graph the solution.

Your Turn!
• Solve 7x + 9 10x – 12

• Graph the solution.

“And” Compound Inequalities
• Solve -2 3t – 8 10

• Graph the solution.

Your Turn!
• Solve -12 3x – 3 15

• Graph the solution.

“Or” Compound Inequalities
• Solve 2x + 3 < 5 or 4x – 7 > 9

• Graph the solution.

Your Turn!
• Solve -2x + 7 < 3 or 3x + 5 < 2

• Graph the solution.

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1. 1.6 Solving Linear Inequalities

2. Graphing One Variable Inequalities • Graph x < 3 • Graph x ≥ -2

3. Solving 1-Variable Inequalities • Solve 5y – 8 12 • Graph the solution.

4. • Solve 2x + 1 6x – 1 Graph the solution.

5. Your Turn! • Solve 7x + 9 10x – 12 • Graph the solution.

6. “And” Compound Inequalities • Solve -2 3t – 8 10 • Graph the solution.

7. Your Turn! • Solve -12 3x – 3 15 • Graph the solution.

8. “Or” Compound Inequalities • Solve 2x + 3 < 5 or 4x – 7 > 9 • Graph the solution.

9. Your Turn! • Solve -2x + 7 < 3 or 3x + 5 < 2 • Graph the solution.