Question

Simplify the expression

$16-2\left|3\right(1-4)-(8-5\left)\right|$

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.

. 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 ,localid="1658066854352" $$\begin{gathered} \left|3(1-4)-(8-5)\right|=\left|3\times -3-3\right| \\ =\left|-9-3\right| \\ =\left|-12\right| \\ Taketheabsolutevalue,weget=12 \end{gathered}$$

. Solving the expression

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

the expression will become

localid="1658066877943" $$\begin{gathered} 16-2\left|3\right(1-4)-(8-5\left)\right|=16-2\times 12 \\ =16-24 \\ =-8,\sin cetheremorenegativesumwillbenegative \end{gathered}$$