To make the equation \( 5x + 12 = __ x + 9 \) have no solution, we need to set the right side in such a way that it cannot equal the left side for any value of \( x \).
One way to do this is to make both sides equal but create a contradiction. For example, we can place a constant that, when simplified, cannot equal the expression on the left side.
Let's choose the right side as follows:
\[ 5x + 12 = 5x + 1 \]
Now let's see if there can be any solution:
- Subtract \( 5x \) from both sides:
\[ 12 = 1 \]
This is a contradiction, as \( 12 \) does not equal \( 1 \).
Thus, the completed equation is:
\[ 5x + 12 = 5x + 1 \]
This gives us an equation with no solution.