To make the equation \(5x - 4 = k\) have no solutions, you can set \(k\) to be a value that is impossible for \(5x - 4\) to equal.
For example, if you set:
\[ 5x - 4 = 5 \]
In this case, rearranging gives:
\[ 5x = 9 \ x = \frac{9}{5} \]
This has a solution. However, if you want to ensure there are no solutions, one method is to set the right side to something that is inconsistent with the left side.
A simple way to do this is to set:
\[ 5x - 4 = 5x + 1 \]
Rearranging gives:
\[ -4 = 1 \]
This statement is false and therefore has no solutions.
Alternatively, you could also set:
\[ 5x - 4 = -4 \]
which yields:
\[ 5x = 0 \ x = 0 \]
This has a solution, so you would need a contradiction.
So a final valid example where the left and right sides are never equal would be:
\[ 5x - 4 = 5x - 5 \]
This gives:
\[ -4 = -5 \]
This is false, indicating that the equation has no solutions.