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Solving Compound Inequalities
6.3 Goal Solve and graph compound inequalities Key Words compound inequality conjunction disjunction
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Definition A compound inequality consists of two inequalities connected by the word and or the word or. Examples -7 < x < x < 8 or x > 27 x < - 4 or x > x 30
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EXAMPLE 1 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.
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Checkpoint Graph 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
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MOUNTAIN PLANT LIFE Compound Inequalities in Real Life
EXAMPLE 2 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
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Solve -2 < x + 2 4. Then graph the solution.
EXAMPLE 3 Solve Compound Inequalities with AND Solve -2 < x + 2 4. Then graph the solution. Method 1
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Solve -2 < x + 2 4. Then graph the solution.
EXAMPLE 3 Solve Compound Inequalities with AND Solve -2 < x + 2 4. Then graph the solution. Method 2
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Checkpoint Use 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
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Solve – 2 < – 2 – x < 1. Then graph the solution.
EXAMPLE 5 Reverse Both Inequalities Solve – 2 < – 2 – x < 1. Then graph the solution.
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Checkpoint Use Subtraction to Solve an Inequality
Solve the inequality. Then graph the solution. 3 2x + 3 7 – 6 – 3x 12
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EXAMPLE 1 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.
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Checkpoint Graph 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
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Solve 3x + 1 4 or 2x – 5 7. Then graph the solution.
EXAMPLE 3 Solve Compound Inequalities with OR Solve 3x + 1 4 or 2x – 5 7. Then graph the solution.
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Solve: x - 4 -8 or x + 3 5. Then graph the solution.
EXAMPLE 3 Solve Compound Inequalities with OR Solve: x - 4 -8 or x + 3 5. Then graph the solution.
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Checkpoint Use 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
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Solve 2 – 10 x -28 or -9x – 6 21. Then graph the solution.
EXAMPLE 5 Reverse Both Inequalities Solve 2 – 10 x -28 or -9x – 6 21. Then graph the solution.
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Homework p. 349 #12-38 evens, 39, 40, 45, 50, 62, 65
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