SOLUTION: Question 1044755: Question 1044751: hello, why does |2x-3| + 4 =2 have no solution. please show steps in coming to that. thanks Answer by MaxWong(13) About Me (Show Sour

Question 1044831: Question 1044755: Question 1044751: hello,
why does |2x-3| + 4 =2 have no solution.
please show steps in coming to that.
thanks
Answer by MaxWong(13) About Me (Show Source):
You can put this solution on YOUR website!
|2x-3|+4=2
|2x-3|=-2
An absolute value of a number, no matter positivity or negativity, could not be a negative number. Therefore no solution.

o.k. thanks, but now why does |x-7|= 12 have the set {19,-5} as a solution. clearly -5 is a negative number.
what am I missing here??
thanks
Answer by Boreal(3362) About Me (Show Source):
You can put this solution on YOUR website!
|x-7|=12
x-7=12; x=19
(x-7)=-12; x=-5
The reason it works is x is negative but |(x-7)| is |(-12)| which is 12.
The absolute value of something can't be negative BUT the absolute value of a negative number is positive and exists.

Thanks for the reply.
So just to be sure, you're saying x and another number inside the hash marks can both be negative, but x by itself, even if in hash marks, cant (be followed by) equal a negative number?
thank you.

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
You can put anything you want in absolute value brackets, including negative numbers. Yes.
But the absolute value of anything cannot be a negative number. Yes.
|-x|=2 No problem. x=-2 and x=2. Both of those become positive in the brackets.
|x|=-2 No. No absolute value of anything can be negative by definition. No matter what goes in the brackets, it cannot come out negative.
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