Question

In the following exercise, simplify.

$12-3\left|1-4\left(4-2\right)\right|$

Short answer

The given absolute value expression is simplified to$-9.$

Step-by-step solution

Step 1.Given information

The absolute expression is$12-3\left|1-4\left(4-2\right)\right|$

Step 2. Concept used

• The modulus of a positive or negative number is always positive.

Step 3.Simplify

$$\begin{gathered} 12-3\left|1-4\left(4-2\right)\right|=12-3\left|1-4\left(4-2\right)\right|\text{simplifyinsidethemodulus} \\ =12-3\left|1-4\left(2\right)\right| \\ =12-3\left|1-8\right| \\ =12-3\left|-7\right| \\ =12-3\left(7\right)\text{Since,}\left|-7\right|\text{=7} \\ =12-21 \\ =-9 \end{gathered}$$

Hence, the simplified value is$-9.$