Maths - Inequalities
Pearson Edexcel Mathematics 2022
See also Maths - Set Notation for InequalitiesA, Maths - RegionsA.
Multiplying and dividing inequalities by signed numbers
What effect does multiplying or dividing an inequality by a positive number have on the symbol?
The symbol is unchanged.
What effect does multiplying or dividing an inequality by a negative number have on the symbol?
The symbol flips, so $> \to <$ and vice versa.
Clearing a variable from the denominator
If you have something such as $\frac{6}{x} > 2$, what should you multiply both sides by?
Why is it sometimes necessary 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.