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

Answer: 5