In the same way that people are never equal (identical looks, wealth, thoughts, sense of humour etc.), not all algebra deals with equations. If you are working in quality control at a factory making cans of cola you will need to check samples of cans which are produced to make sure that they contain the right amount of cola. The can may advertise that it contains 330ml of cola, however there will be a little leeway (sometimes called tolerance) in this measurement as it will be impossible to put exactly 330ml of Cola in each can. For example it may be that the cola factory is allowed to produce cans that contain between 329.5ml and 330.5ml.

In other words the amount of cola has to be greater than 329.5ml and less than 330.5ml.

Written in shorthand this can be shown as:

amount of cola > 329.5ml
amount of cola < 330.5ml

Which can also be written as a single statment:

329.5ml < amount of cola < 330.5ml

To remember which way these funny arrows go, remember that Less than points to the Left. Sometimes the arrows are included with an equals sign >= or <=. Generally speaking, if we say that a is a "thing" and b is another "thing" that:

a < b means a is less than b (so b must be greater than a)
a > b means a is greater than b (so b must be less than a)

a <= b means a is less than or equal to b (so b must be greater than or equal to a)
a >= b means a is greater than or equal to b (so a must be greater than or equal to b)

When solving inequalities all the rules you have learnt which can be used when solving equations apply apart from: If you multiply or divide by a negative number, the inequality sign is reversed.

Example Solve:    2(x + 6) < 4x + 10

 2x + 12 < 4x + 10
        -2x < -2
           x > 1 (sign is reversed because we divided by -2)

Inequalities can be shown on graphs using shading.

If y > 3x, you draw the graph of y = 3x and shade out the bits you don't want (i.e. all the points where y < 3x).