Chapter 3.7, Problem 27PPE

To determine

The solution of the given expression.

Answer to Problem 27PPE

  $y=0,3$

Explanation of Solution

Given information:

The given expression is:

  $4\left|2y-3\right|-1=11$

Calculation:

The solution of the given expression will be:

  $\begin{array}{l}4\left|2y-3\right|-1=11\\ \Rightarrow 4\left|2y-3\right|=11+1\\ \Rightarrow 4\left|2y-3\right|=12\\ \Rightarrow \left|2y-3\right|=\frac{12}{4}\\ \Rightarrow \left|2y-3\right|=3\end{array}$

  $\begin{array}{l}\Rightarrow 2y-3=3\\ \Rightarrow 2y=3+3\\ \Rightarrow 2y=6\\ \Rightarrow y=3\end{array}$ or $\begin{array}{l}\Rightarrow 2y-3=-3\\ \Rightarrow 2y=-3+3\\ \Rightarrow 2y=0\\ \Rightarrow y=0\end{array}$

Thus, the solution is $y=0,3$