Solving Compound Inequalities Involving And

1
Solving Compound Inequalities Involving And

6.4

• Goal
• Solve and graph compound inequalities involving
  and.
• Key Words
• compound inequality

2
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
3

• 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

5

• 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

6

• Solve Compound Inequalities with AND

Solve -2 lt x 2 ? 4. Then graph the
solution. Method 1
7

• Solve Compound Inequalities with AND

Solve -2 lt x 2 ? 4. Then graph the
solution. Method 2
8
Choose a method from Example 3 to solve the
inequality. Then graph the solution.

• -1 lt x 3 lt 7

• -6 ? 3x ? 12

9
Solve the inequality. Then graph the solution.

• 0 lt x 4 ? 12

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• Solve Multi-Step Compound Inequalities

Solve -3 ? 2x 1 ? 5. Then graph the solution.
11

• Reverse Both Inequalities

Solve 2 lt 2 x lt 1. Then graph the
solution.
12
Solve the inequality. Then graph the solution.

• 3 ? 4 x ? 2

Homework p. 345 14-20e, 22-38e, 48,49