Question

How to find x(x-2)<0

Answer 1

x<2

Explanation:

x- 2 <0

x < 2

Answer 2

`0<x<2`

Explanation:

Hi there!

`x(x-2)<0`

Set x(x-2) equal to 0:

`x(x-2)=0`

Solve for x by using the zero product property:

`x(x-2)=0`

`x=0` and
`x=2`

Now, we know that for the inequality
`x(x-2)<0`, one of the following must be true:

1)
`0<x<2`

2)
`x<0` or
`x>2`

To find out which one it is, 1) or 2), we can substitute a value into
`x(x-2)<0` to see if the inequality is true.

For example, 1 takes place in between 0 and 2. If 1 satisfies
`x(x-2)<0`, then
`0<x<2` must be true. If it does not, then
`x<0` or
`x>2` must be true:

`1(1-2)<0\\1(-1)<0\\-1<0`

This inequality is true. Thus,
`0<x<2`.

I hope this helps!