To create an equation that has no solution, we need to manipulate it so that the left side is never equal to the right side for any value of \( x \). One common way to do this is to make the coefficients of \( x \) equal while ensuring that the constant terms differ.
We have:
\[ 5x + 12 = _x + 9 \]
To make the coefficients of \( x \) the same on both sides, we can replace the blank with \( 5x \) (which means left side becomes equal to right side regarding the \( x \) terms). Now we need the constant terms to be different.
If we write the equation as:
\[ 5x + 12 = 5x + 8 \]
Now, we simplify this:
Subtract \( 5x \) from both sides:
\[ 12 = 8 \]
This equation is false (12 does not equal 8), meaning there are no values of \( x \) that satisfy the equation.
Thus, filling in the blank gives us:
\[ 5x + 12 = 5x + 8 \]
This equation has no solution.