Solving Compound Inequalities

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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 lt x lt 10 x lt 8 or x gt 27 x lt
- 4 or x gt 4 12 ? x ? 30
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• 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.
4
Write a verbal sentence that describes the
inequality. Then graph the inequality.

• -2 lt y lt 0

• 7 ? t ? 8

• 4 ? n lt 11

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• 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 Compound Inequalities with AND

Solve -2 lt x 2 ? 4. Then graph the
solution. Method 1
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• Solve Compound Inequalities with AND

Solve -2 lt x 2 ? 4. Then graph the
solution. Method 2
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Choose a method from Example 3 to solve the
inequality. Then graph the solution.

• -1 lt x 3 lt 7

• -6 ? 3x ? 12

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• Reverse Both Inequalities

Solve 2 lt 2 x lt 1. Then graph the
solution.
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Solve the inequality. Then graph the solution.

• 3 ? 2x 3 ? 7

• 6 ? 3x ? 12

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• 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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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

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• Solve Compound Inequalities with OR

Solve 3x 1 ? 4 or 2x 5 ? 7. Then graph
the solution.
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• Solve Compound Inequalities with OR

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

• 7x ? 42 or x 5 ? 7

• x 7 ? 3 or 5x 5 ? 10

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• 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,
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