Solving Compound Inequalities

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Presentation transcript:

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 -7 < x < 10 x < 8 or x > 27 x < - 4 or x > 4 12  x  30

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.

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

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

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

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

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

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

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

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.

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

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.

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.

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

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.

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