To create an equation that has no solution, we want both sides to simplify to a contradiction.
Starting with the initial equation:
\[ -7x - 12 = x + 12 \]
We can manipulate the left side to try finding a contradiction. First, let's get all terms involving \(x\) on one side and constant terms on the other side.
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Add \(7x\) to both sides: \[ -12 = 8x + 12 \]
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Next, subtract \(12\) from both sides: \[ -24 = 8x \]
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Divide by \(8\): \[ x = -3 \]
Now, to adjust this equation to have no solution, we could manipulate it to create an inconsistency.
Let’s modify the equation to something like:
\[ -7x - 12 = x + 24 \]
Now, following similar steps:
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Add \(7x\) to both sides: \[ -12 = 8x + 24 \]
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Subtract \(24\) from both sides: \[ -36 = 8x \]
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Divide by \(8\): \[ x = -4.5 \]
Now, let’s create a contradiction that leads to no solution.
Instead, if we want an equation with no solutions, let’s set:
\[ -7x - 12 = -7x + 12 \]
Now simplifying both sides gives:
\[ -12 \neq 12 \]
This is a contradiction and thus it confirms that the equation has no solution.
So the final answer to your question is:
\[ -7x - 12 = -7x + 12 \]
This modified equation has no solution.