Chapter 3.1, Problem 53WE

To determine

To solve: the given equation for $t$ .

Answer to Problem 53WE

The equation has no solution.

Explanation of Solution

Given information:

Given equation

  $2=6+\left|t\right|$

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

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

More over

  $\begin{array}{l}\left|x\right|=b\\ \Rightarrow x=b\text{or}x=-b\end{array}$

Calculation:

Consider the given equation,

  $2=6+\left|t\right|$

Now, solve the equation as shown,

  $\begin{array}{c}2=6+\left|t\right|\\ 2-6=6+\left|t\right|-6\\ \left|t\right|=-4\end{array}$

Absolute value of any number can not be negative.

So, the equation has no solution.