Name:Date:Period: Topic: Solving & Graphing Compound InequalitiesEssential Question: How does a compound inequality differ from a regular inequality? What is the meaning of “and” and “or” in a compound inequality? Warm-Up:Match the following graphs with its’ corresponding inequality:

1.5 > x a)

2.5 < x

3.x > 10

4.5 ≥ x

5.5 ≤ x

6.x < 10

0

0

0

0

0

5

5

5

- 5

- 5

- 5

- 5

- 5

5

5

10

10

10

10

10

- 10

- 10

- 10

- 10

- 10

b)

d)

e)

c)

Home-Learning Assignment #1 – Review:

Do you remember the difference between and and or on Set Theory?

AND means intersection-what do the two items

have in common?

OR means union-if it is in one item, it is in

the solution

A

A B

B

Compound Inequality

A compound inequality consist of two inequalities connected by

and or or.

Vocabulary:

Graphing Compound

Graphing Compound

Inequalities

Inequalities

Graph x < 4 and x ≥ 2

3 42●

a) Graph x < 4

b) Graph x ≥ 23 42

o

c) What if I Combine the graphs?

●

3 42o

d) Where do they intersect?●

3 42o

Guided Example:

Graph x < 2 or x ≥ 4

3 42●

a) Graph x < 2

b) Graph x ≥ 43 42

o

c) Combine the graphs

3 42o

3 42●

Guided Example:

1) Which inequalities describe the following graph?

-2 -1-3oo

1. y > -3 or y < -1

2. y > -3 and y < -1

3. y ≤ -3 or y ≥ -1

4. y ≥ -3 and y ≤ -1

When written this way, it is the same thing as

6 < m AND m < 8

It can be rewritten as m > 6 and m < 8 and graphed as previously shown.

Lets graph the compound inequality 6 < m < 8

7 86oo

2) Which is equivalent to-3 < y < 5?

1. y > -3 or y < 5

2. y > -3 and y < 5

3. y < -3 or y > 5

4. y < -3 and y > 5

3) Which is equivalent to x > -5 and x ≤ 1?

1. -5 < x ≤ 1

2. -5 > x ≥ 1

3. -5 > x ≤ 1

4. -5 < x ≥ 1

Writing Compound

Writing Compound

Inequalities

Inequalities

All real numbers that are greater than – 2 and less than 6

All real numbers that are less than 0 or greater than or equal to 5

- 2 < x < 6

x < 0 or x ≥ 5

All real numbers that are greater than zero and less than or equal to 4.

40 x

All real numbers that are less than –1 or greater than 2

21 xorx

Guided Example:

6) All real numbers that are greater than or equal to – 4 and less than 6

7) All real numbers that are less than or equal to 2.5 or greater than 6

4) Graph x < 2 or x ≥ 4

5) Graph x ≥ -1 or x ≤ 3

8) x is less than 4 and is at least -9

49.)

49.)

49.)

94.)

xd

xc

xb

xa

Solving & Graphing

Compound Inequaliti

es

3 < 2m – 1 < 9

andand

andand

andand

andandHINT: ONLY “AND” PROBLEMS WILL LOOK LIKE

THIS. “OR” PROBLEMS MUST SAY “OR”

Solving & Graphing

3 < 2m – 1 < 9

0 5-5

Answer:

+ 1 + 1 + 1------------------------------ 4 < 2m < 10 2 2 2

2 < m < 5

7521783 xorx

Answer:7521783 xorx

– 8 – 8 3x > 9 3 3 x > 3

– 5 – 5 2x ≤ 2 2 2 x ≤ 1

866 x

92513 x

- 3 < - 1 – 2x ≤ 511)

12)

13)

-15 ≤ –3x – 21 ≤ 2514)

10832 x752413 xorx10)

9)

Additional Practice:

Page 204 - 206 (1 – 8, 14, 36)

For those who complete the work before time is over, proceed to work on the following problems:Page 204 - 206 (10, 15, 24, 26, 38, 41, 55)

2x < -6 and 3x ≥ 12

1. Solve each inequality for x

2. Graph each inequality3. Combine the graphs4. Where do they

intersect?5. They do not! x cannot

be greater than or equal to 4 and less than -3 No Solution!!

2 6

2 2 3

x

x

3x 12

3 3 x 4

-3 0-6o-3 0-6o

4 71o●4 71o●

Based on the meaning of ‘and,’ why is this No Solution ?

Wrap-Up:Vocabulary Review

Summary

Home-Learning Assignment #2:Page 204 – 206 (9, 16, 18, 37, 54)