A reminder about the existence conditions

Whatever you do with an irrational inequality, the first move is always the same: writing down the existence conditions.

Remark — A reminder about the CE

The first move is always to write down the existence conditions (CE):

• for every root of even index the argument must be $\ge 0$;
• for every denominator the expression must be $\ne 0$.

A solution computed without the CE is, quite simply, a set of candidate values, which must then be intersected with the CE. Throughout the chapter we shall write the CE as the very first thing and bring them back in at the end.

Keeping the CE always under control is what distinguishes a correct answer from a solution set “polluted” by values at which the root does not even exist.

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Topics: Irrational inequalities
Concepts: Existence conditions · Irrational inequality
Skills: Solving inequalities