INEQUALITIES

INEQUALITIES

INTRODUCTION

An inequality says that two values are not equal. 

a ≠ b says that a is not equal to b

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

a < b says that a is less than b

a > b says that a is greater than b

(those two are known as strict inequality) 

a ≤ b means that a is less than or equal to b

a ≥ b means that a is greater than or equal to b.

SOLVING INEQUALITIES

Sometimes we need to solve Inequalities like these:

Symbol	Words	Example
>	greater than	x + 3 > 2
<	less than	7x < 28
≥	greater than or equal to	5 ≥ x - 1
≤	less than or equal to	2y + 1 ≤ 7

SOLVING

Our aim is to have x (or whatever the variable is) on its own on the left of the inequality sign:

Something like:		x < 5
or:		y ≥ 11

We call that "solved".

EXAMPLES SOLVING INEQUALITIES

Example 1:
Alex and Billy have a race, and Billy wins!
What do we know?
We don't know how fast they ran, but we do know that Billy was faster than Alex:

Billy was faster than Alex

We can write that down like this:

b > a

(Where "b" means how fast Billy was, ">" means "greater than", and "a" means how fast Alex was).
We call things like that inequalities (because they are not "equal").

Example 2:
Alex plays in the under 15's soccer. How old is Alex?
We don't know exactly how old Alex is, because it doesn't say "equals"
But we do know "less than 15", so we can write:

Age < 15

The small end points to "Age" because the age is smaller than 15.

Example 3 is equal to:
You must be 13 or older to watch a movie.
The "inequality" is between your age and the age of 13.
Your age must be "greater than or equal to 13", which is written:

Age ≥ 13

Exercise :

Solve x + 5 < 12

Below is the video of Inequalities:

ref:

http://www.mathsisfun.com/definitions/inequality.html

http://www.mathsisfun.com/algebra/inequality-solving.html

https://youtu.be/lo1kvxu-Dc8