Question

How do i solve |x| > -9?

Answer 1

bearing in mind that an absolute value expression is in effect a piece-wise expression, since it has a ± version, then

`\bf |x|>-9\implies \begin{cases}+(x)>-9\implies x>-9\\[-0.5em]\hrulefill\\-(x)>-9\implies x\stackrel{\stackrel{notice}{\downarrow }}{<}9\end{cases}~\hspace{1.2em}\stackrel{\textit{and we can write that as a triplet}}{-9< x < 9}`

recal that with inequalities, when we multiply/divide/exponentialize by a negative value, we flip the inequality sign.