Question

What is the solution to the inequality |3x|>0

Answer 1

|3x|>0
3x> 0 then x > 0
-3x > 0 then x < 0

answer
x > 0 or x < 0

Answer 2

Answer: The required solution is
`x>0~\textup{or}~x<0.`

Step-by-step explanation: We are given to find the solution of the following inequality:

`|3x|>0~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)`

We know that,

If
`|x|>a,` then we have

`x>a~~~~~~\textup{or}~~~~~~x<-a.`

From inequality (i), we get

`|3x|>0\\\\\Rightarrow 3x>0~~~~~\textup{or}~~~~~3x<-0\\\\\Rightarrow x>(0)/(3)~~~~~~~~~~~~\Rightarrow 3x<0\\\\ \Rightarrow x>3~~~~~~~~~~~~~\Rightarrow x<(0)/(3)\\\\\Rightarrow x>3~~~~~~~~~~~~~\Rightarrow x<0.`

Thus, the required solution is
`x>0~\textup{or}~x<0.`