Absolute value

Question

If I'm doing a PEMDAS problem, and there is an absolute value symbol in the problem what should I start with? 

Answer 1

The precedence rules (P-E-M-D-A-S) define the order of operations for an arithmetic expression.

 

Now, when there is an absolute value (for example, |y|) in the expression, you must evaluate the expression twice: (1) once for (+y), and (2) once for (-y).  The expression could be either result.

 

Here's an example:

     2 * |x-3|

 

    case 1:

     2 * (+(x-3))          (evaluate expression inside || using PEMDAS; then +)

    2 * ((+1)*(x-3))   [note: multiplication by (+1) is assumed; distribute]

    2 * (x-3)             (PEMDAS; for Parentheses; remove parentheses)

     2x - 6                 [distributive the multiplication]

 or

    case 2:

    2 * (-(x-3))          (evaluate expression in side || using PEMDAS; then -)

    2 * ((-1)*(x-3))        [note: multiplication by (-1) is assumed; then distribute]

    2 * (-x+3)            [PEMDAS for Parentheses; remove parentheses)

     -2x + 6               [distribute the multiplication]

 

So, the expression is either:

      2x - 6

   or

      -2x + 6

Answer 2

PEMDAS should always be used first. The purpose of of PEMDAS is to accurately simplify the expression/equation.

Simplify means to write the expression/equation with as few symbols as possible.

The use of PEMDAS is applicable to the argument of the absolute value.

Answer 3

Caleb,

 

I would evaluate the absolute value first, then using that value, apply PEMDAS.