Example 2

When applying the order of operations to an expression, absolute value symbols are treated in the same manner as brackets. Evaluate the expression inside the absolute value symbols before applying operations outside of them.

Evaluate the following.

1. \(\left| {12} \right| - \left| { - 15} \right|\)
   
   
   Solution

   \(\begin{align}
    \left| {12} \right| - \left| { - 15} \right| &= 12 - 15 \\
     &= -3 \\  \end{align}\)
   
   
   
2. \(\left| {\left( {3 - 2} \right)^2 - 4} \right| + \left| {12 - 6} \right|\)
   
   
   Solution

   \(\begin{align}
    \left| {\left( {3 - 2} \right)^2 - 4} \right| + \left| {12 - 6} \right| &= \left| {1^2 - 4} \right| + \left| 6 \right| \\
     &= \left| {-3} \right| + 6 \\
     &= 3 + 6 \\
     &= 9 \\  \end{align}\)