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

$|3x|>0\\\\\Rightarrow 3x>0~~~~~\textup{or}~~~~~3x<-0\\\\\Rightarrow x>\dfrac{0}{3}~~~~~~~~~~~~\Rightarrow 3x<0\\\\ \Rightarrow x>3~~~~~~~~~~~~~\Rightarrow x<\dfrac{0}{3}\\\\\Rightarrow x>3~~~~~~~~~~~~~\Rightarrow x<0.$

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