Math is not always about “equal”. Sometimes you may only know that something is bigger or smaller than another value. Statements such as these are called inequalities.
Inequalities tell you about the relative size of a value. This means that an inequality will compare the size of more than one value.
Example:
Alex and Ben have a race, Ben wins.
What so we know from this statement? We do not know how fast Alex or Ben ran, but we do know that Ben ran faster than Alex.
So now if we let the variable b represent Ben’s speed and we let the variable a represent Alex’s speed, then we can write down that Ben was faster than Alex like this:
b > a
There are two common symbols we use then writing inequalities.
These symbols are:
> This symbol means “greater than”. For example, 5 is greater than 2 so we write than 5 > 2.
< This symbol means “less than”. For example, 7 is less than 9 so we write that 7 < 9.
If you are having trouble remembering which symbol is which all you need to know is that the “small” end of the symbol always points to the smaller number.
Example: James plays for the 15 and under soccer team. How old in James?
We do not know exactly how old James is because the question does not say “equals”. But we do know “less than 15”, so we can write:
James’ age < 15
Remember:
The small end points to “James’ age” because his age is a value smaller than 15.
Now we can look at two more important symbols.
These symbols show us that we can also have inequalities that include “equals”.
These two symbols are:
≥ This symbol means “greater than or equal to”. For example, y ≥ 3.
≤ This symbol means “less than or equal to”. For example, x ≤ 6.
Example: To watch a certain movie you must be 13 years old or older.
The “inequality” is between your age and the age of 13.
Your age must be “greater than or equal to 13”, which would be written:
Age ≥ 13
Now, we will see what you have learned.
Write an inequality to answer each of the following questions.
1. Ed and Simon were climbing a tree and Ed reached the top first. What do we know about how fast Ed climbed compared to how fast Simon climbed?
2. Sara is 7 years old and she is the youngest of her sisters. What do we know about all the ages of the girls in Sara`s family?
This article was written for you by Mia, one of the tutors with Test Prep Academy.