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Inequalities and their Graphs. 2. 3. 4. 5. 6. 7. 8. Symbols. How to graph the solutions when the variable is on the left. > Graph any number greater than. . . open circle, line to the right < Graph any number less than . . . open circle, line to the left

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how to graph the solutions when the variable is on the left
How to graph the solutions when the variable is on the left

> Graph any number greater than. . .

open circle, line to the right

< Graph any number less than. . .

open circle, line to the left

Graph any number greater than or equal to. . .

closed circle, line to the right

Graph any number less than or equal to. . .

closed circle, line to the left

slide4

Inequalities and their Graphs

Notice: when variable is on left side, sign shows direction of solution

3

slide5

Inequalities and their Graphs

Notice: when variable is on left side, sign shows direction of solution

7

slide6

Inequalities and their Graphs

Notice: when variable is on left side, sign shows direction of solution

Color in circle

-2

slide7

Inequalities and their Graphs

Notice: when variable is on left side, sign shows direction of solution

8

Color in circle

solutions

-5 -4 -3 -2 -1 0 1 2 3 4 5

Solutions….

You can have a range of answers……

A. All numbers less than 5

B. All numbers that are 5 or less

C. All numbers that are 5 or greater

D. All numbers that are greater than 5

A. X > 5

B. X ≥ 5

C. X < 5

D. X ≤ 5

solutions continued

-5 -4 -3 -2 -1 0 1 2 3 4 5

Solutions continued…

A. All numbers less than -1

B. All numbers that are -1 or less

C. All numbers that are -1 or greater

D. All numbers that are greater than -1

A. X > -1

B. X ≥ -1

C. X < -1

D. X ≤ -1

solutions continued1

-5 -4 -3 -2 -1 0 1 2 3 4 5

Solutions continued….

A. All numbers less than 1

B. All numbers that are 1 or less

C. All numbers that are 1 or greater

D. All numbers that are greater than 1

A. X > 1

B. X ≥ 1

C. X < 1

D. X ≤ 1

solutions continued2

-5 -4 -3 -2 -1 0 1 2 3 4 5

Solutions continued…

A. All numbers less than -3

B. All numbers that are -3 or less

C. All numbers that are -3 or greater

D. All numbers that are greater than -3

A. X > -3

B. X ≥ -3

C. X < -3

D. X ≤ -3

slide12

X < 2

The open circle tells us that 2 is not included

The arrow tells us that everything to the left of 2 is included

Could 3 be a solution?

Could 0 be a solution?

No

yes

slide13

X ≤ 2

The closed circle tells us that 2 is included.

The arrow tells us that everything to the left of 2 is also included.

Could 2 be a solution?

Could 3 be a solution?

Yes

No

slide14

Write an inequality for the above graph.

X ≤-3

Say the inequality in your own words.

X is less than or equal to -3

slide15

Write an inequality for the above graph.

X > 5

Say the inequality in your own words.

X is greater than 5

slide16

You must be at least 42 inches tall to ride the bumper cars.

Write the inequality with h standing for height

h ≥ 42

slide17

Children under 12 can enter the museum at no charge.

Write the inequality

x < 12

If you are 12 can you get in free?

If you are 5 can you get in free?

no

yes

If you are 11 can you get in free?

yes

slide18

To vote in the United States, a person must be 18 years old or older.

Write the inequality

x ≥ 18

Can you vote at 17 years?

no

Can you vote at 95 years?

yes

Can you vote at 18 years?

yes

slide19

Practice:

Worksheet