Why |x-5| =-4 is invalid ? could some one brief here

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Akshay Vyavahare

B.Sc.(I.T.) Diploma of Software Engineer. from NIIT

Hi, |abc| is called Mod symbol.. i.e. value will be absolute (non-negative).. i.e. value inside mod symbol will remain positive. eg. |-5| = 5 So, |x-5|=-4 is invalid.. it can be |x-5|=4.
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IIT/BITSAT Decoded !!

The answer is simple, modulas of anything cannot be negative since mod makes every quantitiy positive .Therefore |x-5| can never be equal to -4.
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Headstart to assured 95+ score in math

| | symbol means modulus. It just gives a positive real no., no matter the no. inside is | | is positive or negative. So there can never be a no. whose modulus is negative.(the modulus of a negative no. can be positive,in fact it is.). Good luck.
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Tutor

When you apply the concept of absolute value to any quantity say a scalar or vector, it returns a scalar value of something like distance and not displacement. Distance does not have direction, thus it can't be negative.
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GMAT Math Expert

Mod of any value inside is always positive. In this case answer is given negative, so it's incorrect.
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BE, R V College Of Engineering, Bangalore.

since modulus is always positive and LHS in above equation contains modulus while RHS is having negative number.so positive quantity can't be equal to negative hence the above equation is invalid.
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When "absolute" of some value is taken ,the resultant value will always be positive,hence the equation itself is not valid as the answer is -4(a negative value)
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Retired from Kendrya vidyalaya.received awards from Kvs for being the best teacher rmore than once

mod x-5 is positive.hence it can't be=-4
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Teaching is my passion!!!!

Modulus is like a machine in which input can be any real no.. But output is always without sign..
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Tutor

The answer should be |x-5| = 4 as modulus of any number is positive. Hence the given expression is invalid.
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