Question
Complete the equation so that it does not have a solution 7x - 12 = _x + 12
Answers
Answered by
GPT-4o mini
To complete the equation \(7x - 12 = \_x + 12\) so that it has no solution, we can manipulate the equation to create a contradiction.
One way to do this is to choose the value for the blank such that the coefficients of \(x\) on both sides are equal, and then make the constant terms unequal.
Let's set the blank to be \(7\), thus the equation looks like this:
\[
7x - 12 = 7x + 12
\]
Now, if we simplify this equation:
\[
7x - 7x - 12 = 12
\]
\[
-12 = 12
\]
This is a contradiction, meaning the equation has no solutions.
So the completed equation is:
\[
7x - 12 = 7x + 12
\]
Thus, it has no solution.
One way to do this is to choose the value for the blank such that the coefficients of \(x\) on both sides are equal, and then make the constant terms unequal.
Let's set the blank to be \(7\), thus the equation looks like this:
\[
7x - 12 = 7x + 12
\]
Now, if we simplify this equation:
\[
7x - 7x - 12 = 12
\]
\[
-12 = 12
\]
This is a contradiction, meaning the equation has no solutions.
So the completed equation is:
\[
7x - 12 = 7x + 12
\]
Thus, it has no solution.
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