LEGACY Inequalities

A-Level Further Pure 1

Advanced Inequalities

When multiplying or dividing an inequality by a negative number you reverse the direction of the inequality sign so you need to be careful.

For a polynomial inequality move all terms to one side then factor/find roots to find critical values then use a sketch to determine correct intervals.

For an algebraic fraction you need to multiply by a positive number. You can do this by multiplying by a square number e.g.

Using Graphs

If you can sketch graphs and you can solve the inequality by observing on the graph when each function is above/below the other. Still work out critical values by solving and use the graph to help with intervals.

Modulus Inequalities

When given you can simply solve by considering the 2 cases:

When given just consider the same 2 cases. or Find critical values where and then sketch the graph

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