Let a, b, c be nonzero real numbers. Find all possible values of \(\displaystyle \frac{a}{|a|} + \frac{b}{|b|} + \frac{c}{|c|} + \frac{abc}{|abc|}\)
+23245 Each one of the individual terms will have either a value of 1 or -1.
If a, b, and c are all positive, then so is abc, so the sum will be 1 + 1 + 1 + 1 = 4
If one of a, b, and c is negative, then so is abc, so the sum will be 0.
If two of a, b, and c are negative, then abc is positive, so the sum will be zero.
If all three are negative, then so is abc, so the sum will be -4.
The possible values are -4, 0, or 4.
