How do you solve and write the following in interval notation: $-4<1/x<= 1$ ?

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Answer 1 · 2018-07-17T14:14:21

We get $(-infty,1/4)$ or $[1,\infty)$

We are doing case work to solve this inequality:

a) $x>0$
in this case we multiply the given inequality by $x$ and we get

$-4x<1$ and $1<=x$

so we have $x > -1/4$ and $x>=1$ so we get $x>=1$ in this case.

b) $x<0$
we multiply by $x<0$

so we get

$-4x>1>=x$

solving this we get

$x<-1/4$ and $x<=1$

so we get the solution

$x<-1/4$

How do you solve and write the following in interval notation: -4<1/x<= 1 -4<1/x<= 1 ?