Variables as Unknown Quantities Examples

For what values of y does y² = 9?

Because a negative number squared gives you a positive result, y could be 3 or -3. Plugging either value into the equation in place of the y will give you the proper solution.

For what values of y is |y| ≤ 1?

This problem is asking what numbers are within 1 unit of 0 in either direction on the number line. Remember, those vertical lines surrounding a number are asking for its absolute value. When you've got a number surrounded, it'll pretty much tell you anything you want to know. In this case, y can be any real number between -1 and 1. In symbols, the answer to this problem is -1 ≤ y ≤ 1.