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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(52813)   (Show Source):
You can put this solution on YOUR website! .
The solution set for |x| > 0 is {x|x cannot be 0}.
Explain why.
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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}.
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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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