To create an equation that has no solution, we need to set it up so that the variable \( x \) cancels out, leaving a false statement.
Starting with the equation:
\[ 5x + 12 = __x + 9 \]
We can set the blank to make both sides have the same variable coefficient but create a contradiction with the constants.
For instance, let’s fill in the blank with \( 5x + 5 \). The equation becomes:
\[ 5x + 12 = 5x + 5 + 9 \]
Now simplifying the right side gives:
\[ 5x + 12 = 5x + 14 \]
Subtracting \( 5x \) from both sides results in:
\[ 12 = 14 \]
This is a false statement, which means the original equation has no solution.
So the completed equation that has no solution is:
\[ 5x + 12 = 5x + 5. \]