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E7 Inequalities - shading
Contributed by: Cason

Use an open circle when the graph does not include the

point such as x > 7 or x < 25.

The inequality sign always opens to the larger number

as in x > 7 is x is greater than 7.  So we shade on the

larger sign.  The sign points to the smaller number as

in x < 25 is x is smaller than 25 so shade smaller.

23

4

24

5

25

6

26

7

27

8

28

9

Use a closed circle when the graph does  include the

point such as x ≥ 7 or x ≤ 25.

The inequality sign always opens to the larger number

as in x ≥ 7 is x is greater than or equal to 7.  So we

shade on the larger sign.  The sign points to the smaller

number as in x ≤ 25 is x is smaller than or equal to 25

so shade smaller.

23

4

24

5

25

6

26

7

27

8

28

9

 B
 A

Greater than, more than (>) 

Less than (<)

 

Greater than or equal to, at least  (≥) 

Less than or equal to, no more than or at most  (≤)

4

4

5

5

at least 5

6

6

C

D

4

4

5

5

6

6

 B
 A

Greater than, more than (>) 

Less than (<)

 

Greater than or equal to, at least  (≥) 

Less than or equal to, no more than or at most  (≤)

4

4

5

5

more than 5

6

6

C

D

4

4

5

5

6

6

 B
 A

Greater than, more than (>) 

Less than (<)

 

Greater than or equal to, at least  (≥) 

Less than or equal to, no more than or at most  (≤)

4

4

5

5

no more than 5

6

6

C

D

4

4

5

5

6

6

 B
 A

Greater than or equal to (≥)

Less than or equal to  (≤)

4

4

5

5

6

6

x < 5

Greater than (>)

Less than (<)

C

D

4

4

5

5

6

6

A

B

Greater than or equal to (≥)

Less than or equal to  (≤)

4

4

5

5

6

6

x ≤ 5

Greater than (>)

Less than (<)

C

D

4

4

5

5

6

6

 B
 A

Greater than or equal to (≥)

Less than or equal to  (≤)

4

4

5

5

6

6

x ≥ 5

Greater than (>)

Less than (<)

C

D

4

4

5

5

6

6

 B
 A

Greater than or equal to (≥)

Less than or equal to  (≤)

4

4

5

5

6

6

x > 5

Greater than (>)

Less than (<)

C

D

4

4

5

5

6

6

 B
 A

-4

-4

-3

-3

-2

-2

x > -3

C

D

-4

-4

-3

-3

-2

-2

 B
 A

-4

-4

-3

-3

-2

-2

x < -3

C

D

-4

-4

-3

-3

-2

-2

 B
 A

-4

-4

-3

-3

-2

-2

x ≤ -3

C

D

-4

-4

-3

-3

-2

-2

 B
 A

-4

-4

-3

-3

-2

-2

x ≥ -3

C

D

-4

-4

-3

-3

-2

-2

 B
 A

20

20

21

21

22

22

x > 21

C

D

20

20

21

21

22

22

 B
 A

20

20

21

21

22

22

x ≥ 21

C

D

20

20

21

21

22

22

 B
 A

20

20

21

21

22

22

x < 21

C

D

20

20

21

21

22

22

 B
 A

20

20

21

21

22

22

x ≤ 21

C

D

20

20

21

21

22

22

Caution!
 B
 A

If the variable is on the other sign, READ from it first

as in read from right to left so 21 < x would be read as

x is greater 21 for shading.

20

20

21

21

22

22

21 > x

C

D

20

20

21

21

22

22

 B
 A

If the variable is on the other sign, READ from it first

as in read from right to left so 21 ≤ x would be read as

x is greater or equal to 21 for shading.

20

20

21

21

22

22

21 ≤ x

C

D

20

20

21

21

22

22

 B
 A

20

20

21

21

22

22

21 < x

C

D

20

20

21

21

22

22

 B
 A

20

20

21

21

22

22

21 ≥ x

C

D

20

20

21

21

22

22

 B
 A

Remember:  Read from the variable first as is

x is less than 5.

 4

 4 

 5

 5

 6

 6

5 > x

C

D

 4

 4

 5

 5

 6

 6

 B
 A

 4

 4 

 5

 5

 6

 6

5 ≤ x

C

D

 4

 4

 5

 5

 6

 6

 B
 A

 4

 4 

 5

 5

 6

 6

5 < x

C

D

 4

 4

 5

 5

 6

 6

 B
 A

 4

 4 

 5

 5

 6

 6

5 ≤ x

C

D

 4

 4

 5

 5

 6

 6

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