UCL Online STEP and AEA Preparation Sessions
Session 6: Handling inequalities
Why is it that there are some inequalities that you would look to solve and other
inequalities that you would look to prove?
It’s clear that the statement
2x + 4 > 10
is true for some values of x and false for other values of x and so you would look to
solve it (find the values of x for which it is true).
There are a number of methods for solving inequalities and these will be covered in
the session. A key point when solving an inequality is to be aware of ‘sign’, i.e. when
and whether an expression is positive or negative.
This statement
x2 + y2 ≥ 2xy
is true for all real values of x and y and you might look to prove that that is the case.
What methods are there for proving an inequality? We’ll look at good style for
proving inequalities. An algebraic proof might start with a statement that everyone
can agree is true and show how the inequality you are proving is a consequence of
that.
Example problem
Solve the inequality
cos  1
 1 where 0    2 and sin  0
sin 