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

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

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Answer 1 · 2015-07-06T21:16:06

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

Explanation:

The answer above follows the definition of the absolute value:

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

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

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