TOPIC 3 : INEQUALITIES

What is Inequalities?

An inequality says that two values are not equal. 

1 ≠ 2 says that 1 is not equal to 2

There are other special symbols that show in what way things are not equal.

1 < 2 says that 1 is less than 2
2 > 1 says that 2 is greater than 1
(those two are known as strict inequality) 

1 ≤ 2 means that 1 is less than or equal to 2
2 ≥ 1 means that 2 is greater than or equal to 1

Inequality tells us about the relative size of two values.

Mathematics is not always about "equals"! Sometimes we only know that something is bigger or smaller

The two most common inequalities are:

Symbol	Words	Example Use
>	greater than	5 > 2
<	less than	7 < 9

They are easy to remember: the "small" end always points to the smaller number, like this:

BIG > small

Greater than symbol shows.

An Example:

      Example 1:

Solve 2x - 5 < 12

Solution:

2x - 5 < 12


First step: (2x - 5) + 5 < 12 + 5
Second step: 2x < 17
Third step: (1/2)2x < (1/2)17

 = x < 17/2

The solution set of the inequality is {x.:.x.<.17/2} which is read as "the set of all x such that x is less than 17/2"

Example 2:

Solve 13 - 3x  10

Solution:

13 - 3x  10


First step: -3x  10 - 13
Second step: -3x  -3
Third step: (-1/3)(-3x)  (-1/3)(-3) (Recall - rule 5)

= x  1

The solution set is {x : x  1}

Example 3:

Solve 14(x-2)  132 - 281x

Solution:

14(x-2)  132 - 281x
First step:14x - 28  132 - 281x
Second step:14x  160 - 281x
Third step: 295x  160
Fourth step: x  160/295

x  32/59

The solution set is {x : x  32/59}.

Questions for inequalities: 

1. 18 < x + 7 ?          

2.  6y < 19 ?          

3. -7y < -20 ?