How do you translate "The absolute value of the difference y and 2" into an algebraic expression?

Jul 6, 2015

From the definition of an absolute value,
$| y - 2 | =$
(a) $= y - 2$ for any $y - 2 \ge 0$ (that is, $y \ge 2$) OR
(b) $= - \left(y - 2\right) = 2 - y$ for any $y - 2 < 0$ (that is, $y < 2$)

Explanation:

The answer above follows the definition of the absolute value:

$| X | =$ (by definition)
(a) $= X$ for non-negative $X$ (that is, $X \ge 0$)values OR
(b) $= - X$ for negative $X$ (that is, $X < 0$)values.