# Maths - Inequalities

> Source: https://ollybritton.com/notes/a-level/maths/topics/inequalities/ · Updated: 2020-11-04 · Tags: maths

See also [Maths - Set Notation for Inequalities](https://ollybritton.com/notes/a-level/maths/topics/set-notation-inequalities/), [Maths - Regions](https://ollybritton.com/notes/a-level/maths/topics/regions/).

##### What affect does multiplying or dividing an inequality by a positive number have on the symbol??
The symbol is unchanged.

##### What affect does multiplying or dividing an inequality by a negative number have on the symbol??
The symbol flips, so $> \to <$ and vice versa.

##### If you have something such as $\frac{6}{x} > 2$, what should you multiply both sides by??
$$
x^2
$$

##### Why is it sometimes neccessary to multiply both sides of an inequality by $x^2$ rather than $x$ in order to eliminate an $x$ in the denominator??
Because otherwise you are making the assumption $x$ is positive, since a negative value would flip the sign.

##### How would you go about solving $\frac{5}{x-3} < 2$??
Multiply both sides by $(x-3)^2$.

##### What is special about squaring something in the context of inequalities??
A real number squared is always positive, so you can be sure that it won't flip a sign.

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