Anything involving any of the expressions:
< less than
> greater than
≤ less than or equal to
≥ greater than or equal to
is an inequality. There are fundamentally two sorts of inequalities:
One sided, or simple inequalities such as 4x-1<3
Two sided inequalities such as
Solving inequalities is a bit like solving equations. For the example above:
Add 1 to both sides
Divide by 4
For the second example:
Add one 1 to ALL sides as shown
To give
Now divide by 4.
In this example, if
where a whole number, it could be any of 2, 3, 4, 5, 6, 7. Notice because of the < sign,
cannot be equal to 1.
Example: Find the largest integer
that satisfies
Add 1 to both sides
Divide by 4
Since
is an integer, the largest integer less that 4.5, it must be 4.