SOLUTION: 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 pu

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(15235) (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.

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