How do you translate "The absolute value of the difference y and 2" into an algebraic expression?

1 Answer
Zor Shekhtman
Jul 6, 2015

From the definition of an absolute value,
#|y-2| = #
(a) #= y-2# for any #y-2>=0# (that is, #y >= 2#) OR
(b) #= -(y-2) = 2-y# for any #y-2<0# (that is, #y < 2#)

Explanation:

The answer above follows the definition of the absolute value:

#|X| =# (by definition)
(a) #= X# for non-negative #X# (that is, #X >= 0#)values OR
(b) #= -X# for negative #X# (that is, #X < 0#)values.

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