Warmups

10 23

x 2( 4) 3( 1)x x

Translate: The product of 7 and m is at most 10

Solve and graph each inequality:

7 2 1 19x

7-4 Compound Inequalities

Objective: To solve and graph “or” inequalities

Compound Inequality

More than one “and” “or”

today

Example 1: x > 2 or x < -4

Graph on the same number line:

These answers These answersor

Example 2

Graph x < 2 or x > 6

TOO

1. x < -3 or x > 4

2. x > 5 or x < 0

3. x > -5 or x < -7

Write your own…

Write a compound inequality for each solution set shown below:

3.

4.

-2 30

0 5

What about…

5. x < 4 or x > -3

6. x > 3 or 4 < x

7. x – 2 < 0 or 2x + 4 > 8

“All numbers”

TOO – Solve and graph

8. 4x – 5 > 7 or 4x – 5 < -9

9. -1 + x < 3 or –x < -4

10. 3n + 11 < 13 or 2n > 5n - 12

x > 3 or x < -1

All numbers

n < 4

AND vs. OR

AND OR

“and” or no word Must say “or”

Both true One or more true

Special case: No solution Special case: All numbers

Homework

Pg. 410 # 26, 27, 28, 31, 33, 37, 38, 40, 41, 42

Math Lab

Inequalities Review

Tic Tac Toe

AND vs. OR

AND OR

“and” or no word Must say “or”

Both true One or more true

Special case: No solution Special case: All numbers

Translate

•The difference of x and 3 is more than 7.

•The product of 3 and y is at least 10.

•A number decreased by 5 is at least 13.

•Twice a number is less than or equal to the number increased by 3

•A number decreased by 8 is at most 1.

Solve and graph

No solution

2 5 2x

Solve and graph

or3 2 5a 7 3 2( 3)a a

-1 10

1; ; 1a or a

Solve and graph

and

x<1

2 4 6x 2 4x x

1

Solve and graph

y > -1 and y < 3

3 2 3y y y

-1 3

Solve and graph

or

All numbers

2 5 7a 2 3a a

Solve and graph

Write a compound inequality for each solution set shown below:

3.-3 60

3; ; 6x or x

Solve and graph

Write a compound inequality for each solution set shown below:

0 5

0 5x

Solve each inequality.

220

5x 50x

10 10x 0x

9 x 9x

Solve each inequality.

6 24

x 16x

3( 2) 4( 3)x x 18x

336

4x 48x

Solve each inequality.

1 4x 5x

2 16

x 18x

3( 3) 4( 2)x x 17x

Determine Value of r.

5(4, )( , 2)

3r r m

7r

3(3, )( ,5)

5r r m

8r