Chapter 1.4, Problem 7CYU

To determine

To solve: the given equation for $y$ . Check the result.

Answer to Problem 7CYU

The value of $y$ in the given equation is $y=15\text{or}y=-7$.

Explanation of Solution

Given information:

Given equation

  $\left|y-4\right|=11$

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

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

Calculation:

Consider the given equation,

  $\left|y-4\right|=11$

Now, solve the equation as shown,

  $\begin{array}{c}\left|y-4\right|=11\\ y-4=11\text{or}y-4=-11\\ y-4+4=11+4\text{or}y-4+4=-11+4\\ y=15\text{or}y=-7\end{array}$

Now, check the result by back substitution.

  $\begin{array}{c}\left|y-4\right|=11\\ \left|15-4\right|=11\\ \left|11\right|=11\\ 11=11\end{array}$

And

  $\begin{array}{c}\left|y-4\right|=11\\ \left|-7-4\right|=11\\ \left|-11\right|=11\\ 11=11\end{array}$

Which is true.

Hence, the value of $y$ in the given equation is $y=15\text{or}y=-7$.