To solve the equation \( 45 = x - 2 \) using inverse operations, you want to isolate \( x \).
The first step is to eliminate the \(-2\) from the right side by performing the inverse operation, which is to add \(2\) to both sides of the equation:
\[ 45 + 2 = x - 2 + 2 \]
This simplifies to:
\[ 47 = x \]
So, the solution is \( x = 47 \).
In summary, the inverse operation used here was the addition of \(2\) to both sides of the equation.