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Homework Statement
##|x^2-2| \leq 1##
Find ##x##
The Attempt at a Solution
##x^2-2\leq 1##
##x \leq \sqrt{3}##
and
##-(x^2-2)\leq 1##
##-x^2+2 \leq 1##
##x \geq 1##
Therefore the solution is ##1 \leq x \leq \sqrt{3}##
However the book gives another solution which is ##-1 \leq x \leq -\sqrt{3}##
I don't know how the latter solution is found out. How can a range be multiplied by ##-1##?