Question

Simplify the expression

16 − 2|3(1 − 4) − (8 − 5)|

Short answer

Simplified form of$16-2\left|3\right(1-4)-(8-5\left)\right|$is$-8$

Step-by-step solution

Given information

Given expression is$16-2\left|3\right(1-4)-(8-5\left)\right|$.

To simplify the given expression first work inside the parenthesis and do absolute value ,then do the rest of the operations.

Step2:Solving the parenthesis and absolute value

when work on the parenthesis we get $$\begin{gathered} (1-4)=-3 \\ (8-5)=3 \end{gathered}$$

Subtract inside the absolute value bars. ,role="math" localid="1644344346900" $$\begin{gathered} \left|3(1-4)-(8-5)\right|=\left|3\times -3-3\right| \\ =\left|-9-3\right| \\ =\left|-12\right|, \\ Taketheabsolutevalue,weget=12 \end{gathered}$$

Step 3:Solving the expression

When $\left|3(1-4)-(8-5)\right|=12$

the expression will becomerole="math" localid="1644344719904" $$\begin{gathered} 16-2\left|3\right(1-4)-(8-5\left)\right|=16-2\times 12 \\ =16-24 \\ =-8,\sin cetheremorenegativesumwillbenegative \end{gathered}$$