What is the largest possible value of y, if y = - | 3 - x | + 5

Given any expression A, absolute value of A, that is |A|, is always positive or 0.

So |3-x| is always positive or 0, thus -|3-x| is always negative or 0.

Since we want the largest value of - | 3 - x | + 5, we must keep - | 3 - x | as large as possible, that is, we must keep  | 3 - x |  as small as possible.

The smallest possible value of  | 3 - x |  is 0. This happens for x=3.

The largest possible value of y = - | 3 - x | + 5 = 0+5 =5

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