Question

How do you solve and write the following in interval notation: `(x-6)^2/x<0?`?

Answer 1

`x` lies in the interval `(-oo,0)`

Explanation:

The inequality `(x-6)^2/x<0`, means `(x-6)^2/x` is negative.

As the numerator `(x-6)^2` is always positive,

`(x-6)^2/x` is negative only if `x` is negative i.e. `x<0`

i.e. `x` lies in the interval `(-oo,0)`