Question

Absolute value bars are grouping symbols. Use the order of operations to evaluate the expression– 3 +|– x + 2| when x = 12.

Short answer

Answer is 7

Step-by-step solution

– What is absolute value and how to determine the value of variable within the absolute value. 

Absolute Value

Absolute value signs make the final result of the operations between them positive. When deciding on the order of operations, treat absolute value bars like parentheses.

|– 3| = 3: The absolute value bars make negative 3 positive.

| 3 | = 3: The absolute value bars leave positive 3 unchanged

– |– 3| = – 3: The absolute value bars make negative 3 positive. Then the negative sign takes effect, and the answer is a negative 3.

– | 3 | = – 3: The absolute value bars leave positive 3 unchanged. Then the negative sign takes effect, and the answer is a negative 3.

Step 2: Is absolute value first in order of operations?

All of the above grouping symbols, as well as absolute value, have the same order of precedence. Perform operations inside the innermost grouping symbol or absolute value first.

Find the value of: – 3 + |– x + 2|

To find the value of x, the term inside the absolute value is evaluated first according to order of operations, then the absolute value of the resulting expression is taken and the resulting equation is again solved using order of operations

$\begin{array}{l}-3+|-x+2|\\ =-3+|-12+2|\\ =-3+|-10|\\ =-3+10\\ =7\end{array}$

– 3 + |– x + 2| = 7