To create an equation that has no solution, we can formulate a situation where both sides of the equation lead to a contradiction.
Let's analyze the given equation:
\(-7x - 12 = ?x + 12\)
To create a no-solution scenario, we want to set the right side in such a way that, regardless of the value of \(x\), both sides become contradictory.
One way to achieve this is to take the left side and add a value to it that creates an equivalent expression but pushes the two sides towards contradiction.
For example:
If we set the right side equal to \(-7x - 12\) with some adjustment such that it contradicts, suppose we put \(7x + 12\):
\(-7x - 12 = 7x + 12\)
Now let's solve this:
\(-7x - 12 = 7x + 12\)
By adding \(7x\) to both sides:
\(-12 = 14x + 12\)
Now, subtract \(12\) from both sides:
\(-24 = 14x\)
This does have a solution. Actually, let's try a simple no-solution contradiction:
Setting it as follows would achieve no solution:
\(-7x - 12 = -7x + 12\)
This doesn't hold because -12 ≠ 12. Therefore, the answer to fill in the blank is:
Answer: -7x + 12.
So the complete equation would be:
\(-7x - 12 = -7x + 12\) which leads to a no-solution scenario.