Solving Compound Inequalities

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