a < b means a is less than b (so b is greater than a)
a < b means a is less than or equal to b (so b is greater than or equal to a)
a > b means a is greater than or equal to b etc.
a > b means a is greater than b etc.
If you have an inequality, you can add or subtract numbers from each side of the inequality, as with an equation. You can also multiply or divide by a constant. However, if you multiply or divide by a negative number, the inequality sign is reversed.
Solve 3(x + 4) < 5x + 9
3x + 12 < 5x + 9
-2x < -3
x > 3/2 (note: sign reversed because we divided by -2)
Inequalities can be used to describe what range of values a variable can be.
E.g. 4 < x < 10, means x is greater than or equal to 4 but less than 10.
Inequalities are represented on graphs using shading. For example, if y > 4x, the graph of y = 4x would be drawn. Then either all of the points greater than 4x would be shaded or all of the points less than or equal to 4x would be shaded.
x + y < 7
and 1 < x < 4 (NB: this is the same as the two inequalities 1 < x and x < 4)
Represent these inequalities on a graph by leaving unshaded the required regions (i.e. do not shade the points which satisfy the inequalities, but shade everywhere else).