Chapter 1.4, Problem 1CYU

To determine

To evaluate: the given expression.

Answer to Problem 1CYU

  $\left|x-8\right|=12$

Explanation of Solution

Given information:

Given expression

  $\left|x-8\right|$

And

  $x=-4$ , and $y=-9$.

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.

  $\left|x-8\right|$

Substitute the value of $x$ in the given expression,

  $\begin{array}{c}\left|x-8\right|=\left|-4-8\right|\\ =\left|-\left(4+8\right)\right|\\ =\left|-12\right|\\ =12\left[\left|-a\right|=a\right]\end{array}$

Hence, the value of the expression is $12$.