Solving Inequalities
Simple inequalities are are very easy to solve. The process in very similar to making
the subject of an equation, bearing in mind to have the inequality instead of the equals sign throughout:
If the
sign is replaced by any of
the 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 inequality
may only be equal to 2 or 4 since
sois greater than 2 and
sois less than 5.
To solve
follow the same procedure as above, obtaining
and note that nowmay be equal to 2, somay be
To solve
follow the same procedure as above, obtaining 2<=x<=5 and note that nowmay be equal to 2 or 5, somay be
To solve
follow the same procedure as above, obtaining
and note that nowmay not be equal to 2 but may be equal to 5, somay be