1. Compound Inequalities Understanding “and”. Understanding “or”.
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2. Conjunctions and Mary had a little lamb and
it followed her to school one day. or
Georgie Porgie ate the pie or
Georgie Porgie pulled out all the plums.
“And” implies that both must occur.
“Or” implies that one or the other will occur, but not necessarily both.
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3. Definition
A compound inequality consists of two inequalities connected by the word and or the word or.
Examples
-7 < x < x < 8 or x > 27
x < - 4 or x >  x  30

4. The graph of a compound inequality with and is the intersection of the graphs of the inequalities.
The graph of a compound inequality with or is the union of the graph of the inequalities.

5. Solve -2 < x + 2  4. Then graph the solution.
EXAMPLE 3
Solve Compound Inequalities with AND
Solve -2 < x + 2  4. Then graph the solution.

6. Solve -2 < x + 2  4. Then graph the solution.
EXAMPLE 3
Solve Compound Inequalities with AND
Solve -2 < x + 2  4. Then graph the solution.

7. Checkpoint Use Subtraction to Solve an Inequality
-1 < x + 3 < 7
-6  3x  12

8. Checkpoint Graph an Inequality in One Variable.
Write a verbal sentence that describes the inequality. Then graph the inequality.
1. y < 0 or y > 5
y < -3 or y > 5
y < 7 or y > 11

9. Solve 3x + 1  4 or 2x – 5  7. Then graph the solution.
EXAMPLE 3
Solve Compound Inequalities with OR
Solve 3x + 1  4 or 2x – 5  7. Then graph the solution.

10. Solve: x - 4  -8 or x + 3  5. Then graph the solution.
EXAMPLE 3
Solve Compound Inequalities with OR
Solve: x - 4  -8 or x + 3  5. Then graph the solution.

11. Checkpoint Use Subtraction to Solve an Inequality
Solve the inequality. Then graph the solution.
7x  42 or x + 5  7
x + 7  3 or 5x + 5  10