Alright, let's solve the given equation step by step and simplify it.
The given equation is:
[tex]\[
\frac{y}{2} + 3 = 2(y - 2)
\][/tex]
First, let's distribute the 2 on the right side of the equation:
[tex]\[
\frac{y}{2} + 3 = 2y - 4
\][/tex]
Next, we aim to get all terms involving [tex]\( y \)[/tex] on one side of the equation and constant terms on the other side. To do this, we subtract [tex]\(\frac{y}{2}\)[/tex] from both sides:
[tex]\[
3 = 2y - 4 - \frac{y}{2}
\][/tex]
To combine the [tex]\( y \)[/tex]-terms on the right side, we need a common denominator. Consider:
[tex]\[
3 = \frac{4y}{2} - 4 - \frac{y}{2}
\][/tex]
Now, combine like terms on the right-hand side:
[tex]\[
3 = \frac{4y - y}{2} - 4
\][/tex]
[tex]\[
3 = \frac{3y}{2} - 4
\][/tex]
Next, isolate the term involving [tex]\( y \)[/tex]. Add 4 to both sides:
[tex]\[
3 + 4 = \frac{3y}{2}
\][/tex]
[tex]\[
7 = \frac{3y}{2}
\][/tex]
To solve for [tex]\( y \)[/tex], multiply both sides of the equation by [tex]\(\frac{2}{3}\)[/tex]:
[tex]\[
y = 7 \cdot \frac{2}{3}
\][/tex]
[tex]\[
y = \frac{14}{3}
\][/tex]
Thus, the value of [tex]\( y \)[/tex] that satisfies the equation is:
[tex]\[
y = \frac{14}{3}
\][/tex]
