Question

In the following exercises, simplify each expression.

$7-\left|5-3\left(4-1\right)-6\right|$

Short answer

$-3$

Step-by-step solution

Step 1. Given Information

The given expression is$7-\left|5-3\left(4-1\right)-6\right|$.

Step 2. Simplify the expression inside the absolute bar. 

• Remove the bracket first by subtracting 1 from 4.

$7-\left|5-3\left(4-1\right)-6\right|=7-\left|5-3\left(3\right)-6\right|$

• Apply the order of operation. Multiply 3 by 3 and then simplify further by adding and subtracting.

$\begin{array}{rcl}7-\left|5-3\left(3\right)-6\right|& =& 7-\left|5-9-6\right|\\ & =& 7-\left|5-15\right|\\ & =& 7-\left|-10\right|\end{array}$

Step 3. Use the definition of the absolute value. 

• Since the absolute value is always greater than and equal to 0, take the absolute value of the obtained value in the previous step.
• Simplify.

$\begin{array}{rcl}7-\left|-10\right|& =& 7-10\\ & =& -3\end{array}$