Chapter 1.4, Problem 36PPS

To determine

To evaluate: the given expression.

Answer to Problem 36PPS

  $12-t\left|3r+2\right|=-36$

Explanation of Solution

Given information:

Given expression

  $12-t\left|3r+2\right|$

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 $t$ , and $r$ in the given expression,

  $\begin{array}{c}12-t\left|3r+2\right|=12-\left(3\right)\left|3\left(-6\right)+2\right|\\ =12-\left(3\right)\left|-18+2\right|\\ =12-\left(3\right)\left|-16\right|\\ =12-\left(3\right)16\left[\left|-a\right|=a\right]\\ =12-48\\ =-36\end{array}$

Hence, the value of the expressionis $-36$ .