# Solve inequalities

An inequality is a statement how the relative size or order of two objects, or about whether they are the same or not.

$a<b$a is less than b.

$a>b$a is greater than b.

$a=b$a is equal to b.

If we add or subtract the same number to each side of an inequality then we don not change the truth of the inequality.

Example

Solve the inequality for a

$a+b>c$

We subtract b from both sides:

$a+b-b>c-b$

$a>c-b$

If we multiply or divide by a negative number than we must reverse the order of the inequality

If c is positive (and not zero) and a < b, then ac < bc and a/c < b/c

If c is negative (and not zero) and a < b, then ac > bc and a/c > b/c

## Video lesson

Solve the inequality -4(x+3)>24