Question

Solve this please. |x|<13

Answer 1

-13 < x < 13

Explanation:

Recall that the definition of absolute value is as follows:

`|x|=\left \{ {{x\,,\,\,\mbox{for}\,\,x\geq 0} \atop {-x\,,\,\,\mbox{for}\,\,x<0}} \right.`

So we just apply this to solve your inequality:

`|x|<13\\\mbox{Case:} \,\,x\geq0\implies x<13\\\mbox{Case:} \,\,x<0\implies -x<13\implies x>-13\\\\\implies -13<x<13`