SOLUTION: rewrite without absolute value for the given conditions: y=|x-3|+|x+2|-|x-5|, if 3 < x

SOLUTION: rewrite without absolute value for the given conditions: y=|x-3|+|x+2|-|x-5|, if 3 < x < 5

Question 1177717: rewrite without absolute value for the given conditions:
y=|x-3|+|x+2|-|x-5|, if 3 < x < 5

Answer by ikleyn(52835) (Show Source): You can put this solution on YOUR website!
.


If  3 < x < 5,  then


    a)  x-3 > 0;  therefore,  |x-3| = x-3;


    b)  x+2 > 0;  therefore,  |x+2| = x+2;


    c)  x-5 < 0;  therefore,  |x-5| = -(x-5).


THEREFORE,


    y = |x-3| + |x+2| - |x-5| = (x-3) + (x+2) + (x-5) = 3x - 6.      ANSWER

Solved, answered, explained and completed.

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