A.8 Interval
Notation &
Solving
Inequalities
Remember, with great power, comes great responsibility.
-Uncle Ben
Interval Notation
[a,b]: A closed interval consists of all real x such that a  x  b
(a,b) : An open interval consists of all real x such that a  x  b
[a,b) :
(a,b]

A half-open or half-closed interval consists
of all real x such that
[a,) : The interval x  a
(,a] : The interval x  a



a x b
a x b
(a,) : The interval x  a


(,a): The interval x  a

Interval Notation
Write the following inequalities in interval notation and
graph on a number line.
1) 2  x  4
2) 3  x  8
3) x  1
4) x  5
Solving Linear Inequalities
Recall that when you multiply or divide by a negative
number, you must change the direction of the inequality.
1) 8  3(2  x)  2x
Linear Inequalities Practice
Solve the following inequality. Write your answer in interval
notation and graph on a number line.
1) 4 x  7  2x  3
2) 13  3x  7  5
3) 5  3x  2  1
1 2x  3 5
4)  

4
2
2
Solving Absolute Value Inequalities
x 3
-6
-5
-4
-3
-2
-1
0
1
2
3
4

u a
a  u  a
Remember: Less ThAND


5
6
Solving Absolute Value Inequalities
x 3
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5

u a
u  a or u  a
Remember: GreatOR


6
Solving Absolute Value Inequalities
2  3x  5  13

-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
Solving Absolute Value Inequalities
1 2x  2  4

-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
More Practice
1) 2  2x  5  15
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
More Practice
2) 2  3x  4  2
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
Absolute Value Inequality Practice
You guys should try some before I give you the HW, k?
Solve, write your answer in interval notation, and graph!
1) 4  2x  4  7
2) 2x  5  7  4
3) 4  3x  3  10
A.8 Interval
Notation &
Solving
Inequalities
Homework#10 :
p.1030
#77 – 99 Odd
Remember, with great power, comes great responsibility.
-Uncle Ben