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6.3Solving Compound Solving Compound
InequalitiesInequalities
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.
Write a verbal sentence that describes the inequality. Then graph the inequality.
CheckpointCheckpoint Graph an Inequality in One Graph an Inequality in One Variable.Variable.
1. -2 < y < 0
2. 7 t 8
3. 4 n < 11
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.
a. Trees below 6000 feet
b. Alpine flowers below 7500 feet
c. No trees or alpine flowers at or below 14,410 feet
EXAMPLE
3 Solve Compound Inequalities with AND
Solve -2 < x + 2 4. Then graph the solution.Method 1
EXAMPLE
3 Solve Compound Inequalities with AND
Solve -2 < x + 2 4. Then graph the solution.Method 2
Choose a method from Example 3 to solve the inequality. Then graph the solution.
CheckpointCheckpoint Use Subtraction to Solve an InequalityUse Subtraction to Solve an Inequality
4. -1 < x + 3 < 7
5. -6 3x 12
EXAMPLE
5 Reverse Both Inequalities
Solve – 2 < – 2 – x < 1. Then graph the solution.
Solve the inequality. Then graph the solution.
CheckpointCheckpoint Use Subtraction to Solve an InequalityUse Subtraction to Solve an Inequality
7. 3 2x + 3 7
8. – 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.
Write a verbal sentence that describes the inequality. Then graph the inequality.
CheckpointCheckpoint Graph an Inequality in One Graph an Inequality in One Variable.Variable.
1. y < 0 or y > 5
2. y < -3 or y > 5
3. y < 7 or y > 11
EXAMPLE
3 Solve Compound Inequalities with OR
Solve 3x + 1 4 or 2x – 5 7. Then graph the solution.
EXAMPLE
3 Solve Compound Inequalities with OR
Solve: x - 4 -8 or x + 3 5. Then graph the solution.
Solve the inequality. Then graph the solution.
CheckpointCheckpoint Use Subtraction to Solve an InequalityUse Subtraction to Solve an Inequality
4. 7x 42 or x + 5 7
5. x + 7 3 or 5x + 5 10
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