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Mastering Graphing and Solving Linear Inequalities

This guide focuses on solving and graphing linear inequalities. Learn about the structure of linear inequalities and the trichotomy property, which dictates that for any two real numbers, one must be less than, equal to, or greater than the other. Additionally, discover addition and subtraction properties of inequalities and their implications when manipulating inequalities. With practical examples and step-by-step methods, you'll gain the skills needed to effectively graph solutions to inequalities like x < 4 and -4 < x < 1.

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Mastering Graphing and Solving Linear Inequalities

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  1. 6.5 Objective: To solve inequalities and graph the solution

  2. Linear Inequalities • A linear inequality is of the form where a, b and c are real numbers

  3. Trichotomy Property For any two real numbers a and b, either a < b a = b a > b Addition/Subtraction Properties If a > b, then a + c > b + c If a < b, then a + c < b + c Properties of Inequalities

  4. The solution to an inequality can be shown using a graph 4 4 4 4 1 4

  5. Example: Graph the following • x < 4 • x > -2 • -4 < x < 1

  6. Solving linear inequalities • Get the variable on the left side by itself • Multiplying or dividing both side by a negative number reverses the inequality symbol

  7. Examples • 4x – 7 > 5 • 5x – 3 < 17

  8. Examples 3. 4. – 3x < 21

  9. Examples 5. 6x – 12 > 8x + 2 6. 2(x – 3) + 5x < 3(x + 2) – 14

  10. HW p. 316/2-12 even, 13 – 54 eoo Review for Test p. 333/ 44-49, 51-55, 59, 60, 63-66

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