# What are Inequalities?

Nov 19, 2014

They are basically regular functions, but instead of equal signs, they use a variant of less than ">" or greater than "<" in place of the equal sign.

To keep things simple, refer to the function:

$y = 2 x + 3$

It is a basic line. Whatever you plug in a value x, it must fulfill a value for y. If x=1, y must equal 5.

Then you have inequalities.

$y \ge 2 x + 3$

Basically, every value for x and y above or on the line will work as an answer. The point (0, 4) is a good answer, because:

$4 \ge 2 \left(0\right) + 3$
$4 \ge 3$

$y \le 2 x + 3$

Because this is $y \le f \left(x\right)$, every value of x and y below or on the line will work as an answer. (0, 0) works because:

$0 \le 2 \left(0\right) + 3$
$0 \le 3$

Finally there are the non-equal inequalities:

$y < 2 x + 3$
$y > 2 x + 3$

Like the previous inequalities, greater than is anything above the line and less than is anything below the line. The main difference? Anything on the line is not an answer.

Referring to point (1,5)
$5 < \mathmr{and} > 2 \left(1\right) + 3$
$5 < \mathmr{and} > 5$
Is false.

Once you remove the "or equal" part, the entire line is not an answer. On a graph, this line is usually dotted to mean that the line is not an answer, but just a boundary on what can be an answer.