SOLUTION: Prove that for n<0<n a. |m/n|=|m|/|n| b. |mn|=|m||n| c. -|m|<=m<=|m|

Algebra ->  Inequalities -> SOLUTION: Prove that for n<0<n a. |m/n|=|m|/|n| b. |mn|=|m||n| c. -|m|<=m<=|m|      Log On


   

Question 1042516: Prove that for n<0 a. |m/n|=|m|/|n|
b. |mn|=|m||n|
c. -|m|<=m<=|m|
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
I will prove only (a). You do the rest....
abs%28x%29+=+x if x > 0; abs%28x%29+=+-x if x < 0. (And of course, abs%280%29+=+0 .)
Given: n < 0.
Case I. m > 0.
===> m%2Fn+%3C+0, and so abs%28m%2Fn%29+=+-%28m%2Fn%29+=+m%2F%28-n%29+=+abs%28m%29%2Fabs%28n%29
Case II. m < 0.
===> m%2Fn+%3E+0, and so abs%28m%2Fn%29+=+m%2Fn+=+%28-m%29%2F%28-n%29+=+abs%28m%29%2Fabs%28n%29.
Case III. m = 0 is trivial after substitution of 0 for m to both sides of the equation.
Hope you get the drift...