If y is greater than or equal to 0, what is the value of x?

1. |x-3| is greater than or equal to y
2. |x-3| is less than or equal to -y




absolute values can't be negative.

this observation alone is actually enough to solve this problem. here's how:

(1): all this tells you is that |x - 3|, an absolute value, is at least some positive number. this isn't much of a restriction, as it could be anything greater than that number, so there's no way you'll get a unique value for x. insufficient.

(2): (-y) is 0 or less, and the absolute value must be at or below this value.
combined with the basic observation that appears in boldface above, this tells you that y must be 0, and that the absolute value itself must also be 0. (think about the other possibilities for (-y) if this doesn't make sense to you right away). therefore, |x - 3| = 0, so x must be 3. sufficient!