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Solving Compound Inequalities

Solving Compound Inequalities. 6.3. Goal Solve and graph compound inequalities Key Words compound inequality conjunction disjunction. Definition A compound inequality consists of two inequalities connected by the word and or the word or. Examples

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Solving Compound Inequalities

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  1. Solving Compound Inequalities 6.3 • Goal • Solve and graph compound inequalities • Key Words • compound inequality • conjunction • disjunction

  2. Definition A compound inequality consists of two inequalities connected by the word and or the word or. Examples -7 < x < 10 x < 8 or x > 27 x < - 4 or x > 4 12  x  30

  3. 1 EXAMPLE • Write Compound Inequalities with AND Write a compound inequality that represents the set of all real numbers greater than or equal to 0 and less than 4. Then graph the inequality.

  4. CheckpointGraph an Inequality in One Variable. Write a verbal sentence that describes the inequality. Then graph the inequality. • -2 < y < 0 • 7  t  8 • 4  n < 11

  5. 2 EXAMPLE • Compound Inequalities in Real Life • MOUNTAIN PLANT LIFE • Write a compound inequality that describes the approximate elevation range for the type of plant life on Mount Rainier, a mountain peak in Washington. • Trees below 6000 feet • Alpine flowers below 7500 feet • No trees or alpine flowers at or below 14,410 feet

  6. 3 EXAMPLE • Solve Compound Inequalities with AND Solve -2 < x + 2  4. Then graph the solution. Method 1

  7. 3 EXAMPLE • Solve Compound Inequalities with AND Solve -2 < x + 2  4. Then graph the solution. Method 2

  8. CheckpointUse Subtraction to Solve an Inequality Choose a method from Example 3 to solve the inequality. Then graph the solution. • -1 < x + 3 < 7 • -6  3x  12

  9. 5 EXAMPLE • Reverse Both Inequalities Solve – 2 < – 2– x < 1. Then graph the solution.

  10. CheckpointUse Subtraction to Solve an Inequality Solve the inequality. Then graph the solution. • 3  2x + 3  7 • – 6  – 3x  12

  11. 1 EXAMPLE • Write Compound Inequalities with OR Write a compound inequality that represents the set of all real numbers less than or equal to -1 or greater than 3. Then graph the inequality.

  12. CheckpointGraph an Inequality in One Variable. Write a verbal sentence that describes the inequality. Then graph the inequality. 1. y < 0 or y> 5 • y < -3 or y> 5 • y < 7 or y> 11

  13. 3 EXAMPLE • Solve Compound Inequalities with OR Solve 3x + 1  4 or 2x – 5  7. Then graph the solution.

  14. 3 EXAMPLE • Solve Compound Inequalities with OR Solve: x - 4  -8 or x + 3  5. Then graph the solution.

  15. CheckpointUse Subtraction to Solve an Inequality Solve the inequality. Then graph the solution. • 7x 42 or x + 5  7 • x + 7  3 or 5x + 5  10

  16. 5 EXAMPLE • Reverse Both Inequalities Solve 2 – 10 x -28 or -9x – 6  21. Then graph the solution.

  17. Homework p. 349 #12-38 evens, 39, 40, 45, 50, 62, 65

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