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Section 6-4. Solve Compound Inequalities. Compound Inequality : Two separate inequalities joined by and or or. • The graph of a compound inequality with and is the intersection of the graphs of the inequalities. • The graphs go TOWARDS each other.

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Section 6-4

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Section 6 4

Section 6-4

Solve Compound Inequalities


Section 6 4

Compound Inequality: Two separate inequalities joined by and or or.

• The graph of a compound inequality with and is the intersection of the graphs of the inequalities.

• The graphs go TOWARDS each other.

• The graph of a compound inequality with

or is the union of the graphs of the inequalities.

• The graphs go AWAY from each other.


Example 1

Example 1

Write and graph compound inequalities:

a) All real numbers that are greater than or equal to -4 and less than 4.

-4 ≤ x < 4

Graph:

-8 -6 -4 -2 0 2 4 6


Example 1 continued

Example 1 Continued

Write and graph compound inequalities:

b) All real numbers that are less than -1 or greater than 2.

x < -1 or x > 2

Graph:

-3 -2 -1 0 1 2 3 4


Example 2

Example 2

Solve a compound inequality with and:

1 < -2x + 3 < 19

-3 - 3 - 3

-2 < -2x < 16

-2 -2 -2

1 > x > -8

-8 < x < 1

Graph:

-8 -6 -4 -2 0 2 4 6

Given

APOI

Simplify

Flip inequalities b/c divided by negative!

MPOI

Simplify


Example 3

Example 3

Solve each inequality separately.

Solve a compound inequality with or:

3x – 2 ≤ -11or 2x + 8 > 16

Graph:

-8 -6 -4 -2 0 2 4 6

Given

Given

+2 +2

- 8 -8

APOI

APOI

Simplify

3x ≤ -9

2x > 8

Simplify

3 3

2 2

MPOI

MPOI

Simplify

Simplify

or

x > 4

x ≤ -3


Homework

Homework

Section 6-4

Pg. 384 – 387

3 – 5

Solve & Prove: 9 – 19 odd

Follow Directions: 21


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