Solve for $r$.
$\begin{array}{l}
r-45=46 \\
r=\square
\end{array}$
We are given a simple linear equation in the variable \(r\):
\[r - 45 = 46\]
The goal is to determine the value of \(r\) that makes this statement true. To do this, we need to isolate the variable \(r\) on one side of the equation. This can be achieved by performing inverse operations. Since 45 is being subtracted from \(r\), we should add 45 to both sides of the equation.
To isolate \(r\), we add 45 to both sides of the equation:
\[r - 45 + 45 = 46 + 45\]
Simplifying the left side, we get:
\[r + 0 = 46 + 45\]
\[r = 46 + 45\]
Now, we perform the addition:
\[46 + 45 = 91\]
Therefore, the value of \(r\) is 91.
We have found that \(r = 91\). To verify, we can substitute 91 back into the original equation:
\[91 - 45 = 46\]
Since 91 minus 45 is indeed 46, our result is correct. Thus, the final value is \(\boxed{91}\).
Solving for an unknown variable is a fundamental skill used in many everyday situations. For instance, if you are saving for a new item that costs \(\$91\) and you have already saved \(\$45\), you need to determine how much more money (\(r\)) you need to save to reach your goal. The equation \(r + 45 = 91\) represents this scenario, and solving it helps you manage your savings effectively.