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6.5 Objective: To solve inequalities and graph the solution

6.5 Objective: To solve inequalities and graph the solution. Linear Inequalities. A linear inequality is of the form. where a, b and c are real numbers. Trichotomy Property For any two real numbers a and b , either a < b a = b a > b. Addition/Subtraction Properties

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6.5 Objective: To solve inequalities and graph the solution

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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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