Solve for $a$.
$30 = 26 - \frac{a}{6}$
We are given the linear equation:
\[30 = 26 - \frac{a}{6}\]
Our goal is to isolate the variable \(a\). This involves simple algebraic rearrangement using basic arithmetic operations. We will first isolate the term involving \(a\) and then solve for \(a\) itself.
To isolate the term with \(a\), we subtract 26 from both sides of the equation:
\[30 - 26 = -\frac{a}{6}\]
\[4 = -\frac{a}{6}\]
Now, to isolate \(a\), we multiply both sides of the equation by \(-6\):
\[4 \times (-6) = \left( -\frac{a}{6} \right) \times (-6)\]
\[-24 = a\]
Thus, we have found that \(a = -24\).
Imagine you are tracking the water level in a tank. If the level was initially at 30 units, and it drops at a rate of \(\frac{1}{6}\) units per minute for \(a\) minutes, ending at 26 units, you can model the situation with \(30 = 26 + \frac{a}{6}\) or, in this case, a slight variation like the one given. Solving for the time \(a\) helps you understand exactly how long the process took, which is a common task in engineering and physics when managing liquid or resource levels.