How do you solve abs(x-6)< -12?

2 Answers
May 5, 2018

There are no real solutions for the given relation.

Explanation:

The absolute value of anything is >=0

Therefore, specifically abs(x-6) >= 0

So abs(x-6) can not be < -12

May 5, 2018

No solutions for x

Explanation:

First of all there are some rules to be taken in mind while solving modulus inequalities.

One of the basic rules is that : If x in R then |x| != -a where a in R.
This means simply that |anything| cannot be negative.

This is because mod converts every number inside, be it positive or negative, to positive. Just like squaring...

For eg. |5| = 5
and |-5| = 5

So even if x is negative |x| will always be positive.

Now coming back to the question, we have :

|x-6| < -12

That means |x-6| is lesser than -12 or simply is negative, which is absurd as mod of anything cannot be negative.

That means x doesn't have any Real solutions (Solutions that are counted in Real numbers)

:. x has no solutions.