# 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