Question

How do you solve `1/x<4` using a sign chart?

Answer 1

Solution : `x<0 or x >1/4 or (-oo,0) uu(1/4,oo)`

Explanation:

`1/x <4 or 1/x-4 <0 or (1-4x)/x <0` critical points are

`x=0 , 1-4x=0 or x=1/4` . Function is undefined at `x=0`

Sign chart :

When `x<0` sign of `(1-4x)/x` is `(+/-) = - ; <0`

When `0< x<1/4` sign of `(1-4x)/x` is `(+/+) = + ; >0`

When `x >1/4` sign of `(1-4x)/x` is `(-/+) = - ; <0`

Solution : `x<0 or x >1/4 or (-oo,0) uu(1/4,oo)` [Ans]