MODERATE EXERCISES

(3) Simplify the following expressions. 


 (a) 

 (b) |7r - 7s| - |r - s| - 2|3(r - s)|

 (c) a - b + |a - b| - |b - a|
SOLUTION: 

 (a) 

     = |x|
       --- = 1
       |x|

 (b) |7r - 7s| - |r - s| - 2|3(r - s)|

     = 7|r - s| - |r - s| - 2(3)|r - s|

     = 7|r - s| - |r - s| - 6|r - s|

     = (7 - 1 - 6)|r - s|

     = 0

(c)  a - b + |a - b| - |b - a|

     = a - b + |a - b| - |a - b|

     = a - b

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