INEQUALITIES

Introduction to Inequalities

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.

Greater or Less Than

The two most common inequalities are:

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

... Or Equal To!

We can also have inequalities that include "equals", like:

Symbol	Words	Example Use
≥	greater than or equal to	x ≥ 1
≤	less than or equal to	y ≤ 3

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:

Represent the following sentence into inequalities:-

a) To watch a parental guidance movie, you must be 18 years and above.

b) Ali is twice older than Hisyam