Chapter 1.4, Problem 37PPS

To determine

To evaluate: the given expression.

Answer to Problem 37PPS

  $2q+\left|2rt+q\right|=28$

Explanation of Solution

Given information:

Given expression

  $2q+\left|2rt+q\right|$

And

  $q=-8,r=-6$ , and $t=3$ .

Concept used:

Absolute value of a function a is given by

  $\left|a\right|=\{\begin{array}{l}aa>0\\ -aa<0\\ 0a=0\end{array}$ \

And

  $\begin{array}{l}\left|-a\right|=a\\ \left|a\right|=a\end{array}$

Calculation:

Consider the given expression.

  $12-t\left|3r+2\right|$

Substitute the value of $q,t$ , and $r$ in the given expression,

  $\begin{array}{c}2q+\left|2rt+q\right|=2\left(-8\right)+\left|2\left(-6\right)\left(3\right)+\left(-8\right)\right|\\ =-16+\left|-36-8\right|\\ =-16+\left|-44\right|\\ =-16+44\left[\left|-a\right|=a\right]\\ =28\end{array}$

Hence, the value of the expression is $28$ .