SOLUTION: The solution set for |x| > 0 is {x|x cannot be 0}. Explain why.

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Question 1207732: The solution set for |x| > 0 is {x|x cannot be 0}.
Explain why.
Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52814)   (Show Source): You can put this solution on YOUR website!
.
The solution set for |x| > 0 is {x|x cannot be 0}.
Explain why.
~~~~~~~~~~~~~~~~~~~ 

Take x from the given set  {x | x =/= 0}.

Then |x| > 0.


Thus, we proved that  

    if x is from the set {x | x=/= 0}, then the inequality |x| > 0 is valid.



Vice versa, let |x| > 0.   

Any real number, different from 0, satisfies this inequality.


Thus, we proved that 

    if |x| > 0, then  x  belongs to the set  {x | x=/= 0}.  



It means that the solution set for |x| > 0  is {x | x=/=0}.

---------------

Solved in full and explained completely.



Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

{x|x cannot be 0} seems a bit vague in terms of what x is

I assume your teacher meant to write "x is a real number" either in word form or symbolic form.

Basically if |x| > 0 then x is any real number but 0.
Eg: x = 5 since |5| > 0 is true.

Why does this work? Because any real number on the number line is some positive distance away from zero.
|x| represents the distance x is from 0.

Other examples
|-27| = 27, showing -27 is 27 units away from 0.
|4| = 4, showing 4 is 4 units away from 0.

x = 0 isn't allowed unless there was an "or equal to" as part of the inequality sign.
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