91Ó°ÊÓ

Subtract 4 from both the sides of the given equation.

$\begin{array}{c}2\left|2y−6\right|+4−4=8−4\\ 2\left|2y−6\right|=4\end{array}$

Divide each side of the given equation by 2 and simplify.

$\begin{array}{c}\frac{2\left|2y−6\right|}{2}=\frac{4}{2}\\ \left|2y−6\right|=2\end{array}$

For any real numbers p and q, where $qâ‰\yen 0$,

Case 1) if $\left|p\right|=q$ then $p=q$ or

Case 2) if $\left|p\right|=q$ then $p=-q$

Apply case 1 mentioned in step 3 to $\left|2y-6\right|=2$ and simplify.

$\begin{array}{c}2y−6=2\\ 2y−6+6=2+6\\ \frac{2y}{2}=\frac{8}{2}\\ y=4\end{array}$

Apply case 2 mentioned in step 3 to $\left|2y-6\right|=2$ and simplify.

$\begin{array}{c}2y−6=−2\\ 2y−6+6=−2+6\\ \frac{2y}{2}=\frac{4}{2}\\ y=2\end{array}$

To check whether the obtained value of x is the solution of given equation, substitute $4$ for $y$ into $2\left|2y-6\right|+4=8$ and simplify.

$\begin{array}{d}2\left|2\left(4\right)−6\right|+4=8\\ 2\left|8−6\right|+4\stackrel{?}{=}8\\ 2â‹\dots 2+4\stackrel{?}{=}8\\ 4+4\stackrel{?}{=}8\\ 8=8\end{array}$

To check whether the obtained value of x is the solution of given equation, substitute $2$for $y$into $2\left|2y-6\right|+4=8$and simplify.

$\begin{array}{d}2\left|2\left(2\right)−6\right|+4=8\\ 2\left|4−6\right|+4\stackrel{?}{=}8\\ 2â‹\dots 2+4\stackrel{?}{=}8\\ 4+4\stackrel{?}{=}8\\ 8=8\end{array}$

Therefore, the solution set of given equation is $\left\{2,4\right\}$.