Compound Inequalities Chapter 4.8 Part 1

Definition Compound Inequalities are two inequalities

joined by the words “and” or “or”.

When do we need compound inequalities?

The number of questions on the next test will be at least 10 and at most 30.

x = number of questions

x 10 and x 30

Two inequalities in one problem!

Joining Two Inequalities

10 x 30

0 10 20 30 40

Instead of writing x > 10 and x < 30 separately, write in one equation:

Solving Compound Inequalities12 > –3w and –2w > –12 Solve each

separately

12 3

3 3

w

4 w

2 12

2 2

w

6w AND

Graphing “And” Compound Inequalities

4 w 6w AND

-6 -4 -2 0 2 4 6 8

How do we do this? 2 < 5 – f < 5 Divide this into 2 inequalities and solve each.

Then, graph all the values that make both the first one true AND the second one true.

It is still an “AND” Compound Inequality, even though the word “AND” is not present.

For example: 2 < 5 – f < 5 2 < 5 – f AND 5 – f < 5

-5 -5

-3 < – f 3

1 1

f

3 f AND

0

1 1

f

0f

– f < 0-5 -5

3 f AND 0f

-1 0 1 2 3 4

Solving Compound Inequalities using “or” – a > 1 or 3a >12

Solve each inequality. Graph all the solutions that make the first one true OR the second one true.

Solving Compound Inequalities with “or” – a > 1 or 3a > 12 Solve

Separately Divide by coefficient. If negative, switch sign.

1

1 1

a

1a

3 12

3 3

a

4a

Graphing Compound Inequalities with “or”

or

-2 -1 0 1 2 3 4 5

a < -1 a > 4

Writing Inequalities to Match Graphs:

0 2 4 6

-3 -2 -1 0 1 2

x < 0 x > 4OR

x > -1 x < 1AND

Homework

page 198 (13–24 all) Show work!

Due tomorrow.