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Question
Complete the equation so that it has no solution.(1 point)
−7 x − 12= _x + 12

Answer 1

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.