absolute value question

Question

9-(|m|+7)=4

I know that the answer to this problem is "no solution", but I don't know how to end up with that answer. Can someone please explain it to me?

Answer 1

9 - (|m| + 7) = 4    [distribute]

9 - |m| - 7 = 4    [combine constants]

2 - |m| = 4    [subtract 2]

-|m| = 2    [multiply by -1]

|m| = -2

 

No mater what number m is, the absolute value of m will always be non-negative (i.e. greater then or equal to zero.) There are no numbers whose absolute value is -2. Therefor there is no value of m such that this equation could ever be true. "No solution."

Answer 2

9-(|m|+7)=4

9-4=|m|+7

5=|m|+7

There is no number greater than or equal to zero, that is, an absolute value, 

which, when added to 7 gives 5.

Answer 3

Hey Abaline -- the ( ) must become a "5" to shrink 9 into 4 ...

 

when m=0 the ( ) is at it's smallest (7) ... any other m grows the ( ) > 7 ... Regards :)