See also [[Maths - Set Notation for Inequalities]]S , [[Maths - Regions]]S .
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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date: 2020-11-04 16:45
tags:
- '@?maths'
- '@?public'
title: Maths - Inequalities