how to solve: |x-4|

Question

how to solve: |x-4|<a  , where a belongs to real number.Solve by considering different cases depending upon 'a' is negative,positive or zero.
Please can anyone help me to solve this question

anonymous · Answer

Case1:  a<0, a is negative

notice that |x-4| is never negative so the inequality |x-4|<a will not have a solution.

anonymous · Answer

If  |x-4|>a  then x-4>a  or  -(x-4)>a  so x>a+4 
or  -x+4>4  -x>0  x<0  Am i right?

anonymous · Answer

why are you changing the question?

anonymous · Answer

the original question is asking "how to solve |x-4|<a...."

anonymous · Answer

am sorry by mistake

anonymous · Answer

yours is right

anonymous · Answer

ya i got till there but how to get their union?

anonymous · Answer

the union is just considering all the sets in one set and the other... that is the result of the conjunction "OR" .. (as opposed to the "AND" conjunction)

anonymous · Answer

i think an example would explain things better... do you have an example or do you want me to make one up?

anonymous · Answer

hey i would be thankful if u explain the solution of this question as u wish like with an example

anonymous · Answer

am not getting how to compile the two sets

anonymous · Answer

great...
let's consider this case:  |x-2| < 5
is this ok?

anonymous · Answer

ok

anonymous · Answer

lemme ask you this basic question..

what is the solution to |x| < 5

anonymous · Answer

it means that it includes all the points which are less than 5 units from zero right?

anonymous · Answer

on a number line

anonymous · Answer

it means all x LESS than 5 AND all x GREATER than -5
now it's correct... sorry for the incorrect response earlier...

anonymous · Answer

ya

anonymous · Answer

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