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Write out the interval notation
from the overlapping segment, if
any
...


x<3

0

x ≥ −4

Interval Notation:

* Graph the inequalities
separately
...


* Look for everything shaded on
the graph
...

Write out the interval notation
from the number line
...


x +1 −1 < 9 −1

x<8

0

2

8

* Graph the inequalities
separately
...


0

4

0

8

4

8

* Look for overlapping of the
graph
...

Write out the interval notation
from the overlapping segment, if
any
...


x +1−1 < 2 −1

x <1

x>4
x < 1 or x > 4

Interval Notation:

0

1

0

1

6

4

* When two inequalities joined by
“or”, that means union of the
solutions
...

* Look for everything shaded on
the graph
...

Write out the interval notation
from

This instructional aid was prepared by the Learning Commons at Tallahassee Community College

5

−5 < x+3< 9

Example (5):

Solution: This is a three-part inequality
...
However, our goal is to isolate the variable x in the middle
...


−5−3 < x +3−3 < 9−3
−8 < x < 6
-8

0

*State the solution in interval
notation
...
)

6

(−8,6)

− 2 < 7 − 3x ≤ 19

Example (6):

Solution: This is a three-part inequality, so our goal is to isolate the variable x in the
middle
...


− 9 − 3x 12
≥
>
−3 −3 −3

*Next we need to divide -3 in the
middle as well as two sides and
Reverse the inequality symbol
...
(you can graph the
solution to help you write out the
interval notation
...
Write the solution in interval notation
...
2 x + 1 ≤ −1 or 2 x + 1 ≥ 3

2
...
2t − 3 ≥ 5t − (2t + 1)

4
...


3
(1 − x ) ≤ 1 − x
4
2

Answers:
1
...
[− 3,3)

3
...
(− ∞,2)

5
5

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