O Level Maths Notes: Solving Inequalities

Simple inequalities are are very easy to solve. The process in very similar to makingthe subject of an equation, bearing in mind to have the inequality instead of the equals sign throughout:

If thesign is replaced by any ofthe process is identical.

If we ever have to divide or multiply by a minus number the sign has to point the other way. For example

The above equations are “one sided” inequalities but there are also “two sided” inequalities such as

To solve these inequalities we have to makethe sole term of the central term

We add one to obtain

Then divide by 2 to obtain

It may be required, ifis a whole number or integer, to write down all the values ofwhich satisfy the inequality.

For the inequalitymay only be equal to 2 or 4 sincesois greater than 2 andsois less than 5.

To solvefollow the same procedure as above, obtainingand note that nowmay be equal to 2, somay be

To solvefollow the same procedure as above, obtaining 2<=x<=5 and note that now may be equal to 2 or 5, somay be

To solvefollow the same procedure as above, obtainingand note that nowmay not be equal to 2 but may be equal to 5, somay be