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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 lt x lt 10 x lt 8 or x gt 27 x lt

- 4 or x gt 4 12 ? x ? 30

- 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.

- -2 lt y lt 0

- 7 ? t ? 8

- 4 ? n lt 11

- 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 Compound Inequalities with AND

Solve -2 lt x 2 ? 4. Then graph the

solution. Method 1

- Solve Compound Inequalities with AND

Solve -2 lt x 2 ? 4. Then graph the

solution. Method 2

Choose a method from Example 3 to solve the

inequality. Then graph the solution.

- -1 lt x 3 lt 7

- -6 ? 3x ? 12

- Reverse Both Inequalities

Solve 2 lt 2 x lt 1. Then graph the

solution.

Solve the inequality. Then graph the solution.

- 3 ? 2x 3 ? 7

- 6 ? 3x ? 12

- 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.

1. y lt 0 or y gt 5

- y lt -3 or y gt 5

- y lt 7 or y gt 11

- Solve Compound Inequalities with OR

Solve 3x 1 ? 4 or 2x 5 ? 7. Then graph

the solution.

- Solve Compound Inequalities with OR

Solve x - 4 ? -8 or x 3 ? 5. Then graph

the solution.

Solve the inequality. Then graph the solution.

- 7x ? 42 or x 5 ? 7

- x 7 ? 3 or 5x 5 ? 10

- 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

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