$\begin{array}{c}\frac{v}{6}-3=9 \\ \frac{\pm 3+3}{\frac{v}{6}}=\frac{12}{6} \\ v=2\end{array}$
To solve the linear equation \(\frac{v}{6} - 3 = 9\), we aim to isolate the variable \(v\). The equation involves a constant term and a term where the variable is divided by 6. Our strategy is to perform inverse operations to move constants to one side and isolate \(v\).
We start by isolating the term containing the variable \(v\). To do this, we add 3 to both sides of the equation:
\[\frac{v}{6} - 3 + 3 = 9 + 3\]
Simplifying both sides, we get:
\[\frac{v}{6} = 12\]
Now that we have \(\frac{v}{6} = 12\), we need to isolate \(v\) by eliminating the denominator 6. We achieve this by multiplying both sides of the equation by 6:
\[6 \times \left(\frac{v}{6}\right) = 12 \times 6\]
This results in:
\[v = 72\]
Suppose you have a collection of stickers that you decide to distribute equally into 6 envelopes, and after removing 3 stickers for yourself, you are left with 9 stickers to put into the envelopes. By solving \(\frac{v}{6} - 3 = 9\), where \(v\) represents the total number of stickers, we find that you started with \(72\) stickers. This type of algebraic modeling helps in real-life inventory or resource management, where you need to calculate an initial total based on known distribution and subtraction processes.