Solve for $r$.
$-48 = r - 54$
$r = \square$
The problem asks to solve the linear equation \(-48 = r - 54\) for the unknown variable \(r\). This equation represents a relationship where \(r\) is reduced by 54 to result in \(-48\). Our goal is to isolate \(r\) by reversing this operation.
To isolate \(r\), we need to eliminate the \(-54\) on the right side of the equation. We do this by adding 54 to both sides:
\[ -48 + 54 = r - 54 + 54 \]
Since \(-54 + 54 = 0\), the equation simplifies to:
\[ -48 + 54 = r \]
Performing the arithmetic on the left side, we have \(-48 + 54 = 6\), which gives:
\[ 6 = r \]
Thus, the value of \(r\) is 6. We can verify this by plugging it back into the original equation: \(6 - 54 = -48\), which confirms our result.
Imagine you are tracking the temperature throughout the day. If the temperature dropped by \(54^\circ\text{C}\) and ended up at \(-48^\circ\text{C}\), you can use the equation \(r - 54 = -48\) to determine the starting temperature \(r\). By adding \(54^\circ\text{C}\) to the final temperature, you find that the initial temperature was \(6^\circ\text{C}\). This type of calculation is common in meteorology or engineering when dealing with shifts or changes in values.