Answer
The solutions are $y = \frac{15}{2}$ and $y = -\frac{9}{2}$.
Work Step by Step
Use the rule $\quad |a|=b \implies a=b \text{ or } a=-b \quad$ to obtain:
$2y - 3 = 12$ or $2y - 3 = -12$
Now, we solve each equation.
For the first equation we have:
$2y - 3 = 12$
$2y = 3 + 12$
$2y = 15$
Divide both sides of the equation by $2$ to solve for $y$:
$y = \frac{15}{2}$
For the second equation:
$2y - 3 = -12$
$2y = 3 - 12$
$2y = -9$
Divide both sides of the equation by $2$ to solve for $y$:
$y = -\frac{9}{2}$
Checking:
For $y=-\frac{9}{2}$:
\begin{align*}
\left|2\left(-\frac{9}{2}\right)-3\right|&=12\\
\left|-9-3\right|&=12\\
\left|-12\right|&=12\\
12&=12\end{align*}
For $y=\frac{15}{2}$:
\begin{align*}
\left|2\left(\frac{15}{2}\right)-3\right|&=12\\
\left|15-3\right|&=12\\
\left|12\right|&=12\\
12&=12\end{align*}
Therefore, the solutions are $y = \frac{15}{2}$ and $y = -\frac{9}{2}$.
