For what values of x does |x-4| = 4-x?
4-x is the DIFFERENCE between 4 and x.
A DIFFERENCE can be negative, 0, or positive.
|x-4| is the DISTANCE between x and 4.
A DISTANCE must be greater than or equal to 0.
For the DIFFERENCE between two values to be equal to the DISTANCE between the two values, the DIFFERENCE -- like the DISTANCE -- must be greater than or equal to 0:
4-x ≥0
4 ≥ x.
Thus, |x-4| = 4-x when x≤4.
Last edited by
GMATGuruNY on Sun Sep 16, 2012 3:15 am, edited 1 time in total.
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