Question

In the following exercises, simplify each expression.

$8-\left|2-4\left(4-1\right)+3\right|$

Short answer

1

Step-by-step solution

Step 1. Given Information

The given expression is$8-\left|2-4\left(4-1\right)+3\right|$.

Step 2. Simplify the expression inside the absolute bar.

• Remove the bracket first by subtracting 1 from

$8-\left|2-4\left(4-1\right)+3\right|=8-\left|2-4\left(3\right)+3\right|$

• Apply the order of operation. Multiply 4 by 3 and then simplify further by adding and subtracting.

$\begin{array}{rcl}8-\left|2-4\left(3\right)+3\right|& =& 8-\left|2-12+3\right|\\ & =& 8-\left|5-12\right|\\ & =& 8-\left|-7\right|\end{array}$

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.
• $\begin{array}{rcl}8-\left|-7\right|& =& 8-7\\ & =& 1\end{array}$
  

Step 4. Conclusion

The resultant value is 1.