Warm Up• Use the numbers: -5, -4, -3, -2, -1, 0, 1, 2, 3, 4,

5 to answer the following questions.1. What numbers are less than or equal to –1 AND

greater than or equal to –2?2. Which numbers are greater than 1 OR less than

–3?3. Which numbers are less than or equal to –2

AND less than or equal to 2?4. Which numbers are greater than –1 OR greater

than 3?

Warm Up Answers• Use the numbers: -5, -4, -3, -2, -1, 0, 1, 2, 3, 4,

5 to answer the following questions.1. What numbers are less than or equal to –1 AND

greater than or equal to –2? –2, -12. Which numbers are greater than 1 OR less than

–3? -5, -4, 2, 3, 4, 53. Which numbers are less than or equal to –2

AND less than or equal to 2? –5, -4, -3, -24. Which numbers are greater than –1 OR greater

than 3? 0, 1, 2, 3, 4, 5

ObjectivesThe student will be able to:

1. solve compound inequalities.

2. graph the solution sets of compound inequalities.

Designed by Skip Tyler, Varina High SchoolModified by Lisa Hoffmann Troy Buchanan High School

What is the difference between and and or?

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

1) Graph x < 4 and x ≥ 2

3 42●

a) Graph x < 4

b) Graph x ≥ 23 42

o

c) Combine the graphs

●

3 42o

d) Where do they intersect?●

3 42o

2) 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●

3 42●o

3) Which inequalities describe the following graph?

-2 -1-3oo

Answer NowAnswer Now

1. y > -3 or y < -1

2. y > -3 and y < -1

3. y ≤ -3 or y ≥ -1

4. y ≥ -3 and y ≤ -1This is also:

-3 < 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, however,

it is easier to graph everything

between 6 and 8!

4) Graph the compound inequality 6 < m < 8

7 86oo

5) 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

Answer NowAnswer Now

6) 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

Answer NowAnswer Now

7) 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

4 71o4 71o

-3 0-6o

8) Graph 3 < 2m + 1 < 9

Remember, when written like this, it is an AND problem!

3 < 2m + 1 AND 2m + 1 < 9

Solve each inequality.

Graph the intersection of 1 < m and m < 4.

2 41oo

8) Graph 3 < 2m + 1 < 9

Another Way:

Solve for m in the middle

3 < 2m + 1 < 9

-1 -1 -1

2 41oo

2 < 2m < 8

1 < m < 4

9) Graph x < 2 or x ≥ 4

0 5-5

10) Graph x ≥ -1 or x ≤ 3

The whole line is shaded!!

0 5-5