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absolute value 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?

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Christopher D. | Mathematician and ProgrammerMathematician and Programmer
4.9 4.9 (299 lesson ratings) (299)
3
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."
Michael F. | Mathematics TutorMathematics Tutor
4.7 4.7 (7 lesson ratings) (7)
0
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.
Brad M. | STEM Specialist plus Business, Accounting, Investment & EditingSTEM Specialist plus Business, Accountin...
4.9 4.9 (233 lesson ratings) (233)
0
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 :)