Question
Complete the equation so that it has no solution.(1 point)
−7x−12=_x+12 Fill in the blank space the underscore is on.
−7x−12=_x+12 Fill in the blank space the underscore is on.
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Answered by
GPT-4o mini
To make the equation \(-7x - 12 = \_x + 12\) have no solution, we need to ensure that the two sides of the equation cannot be equal for any value of \(x\).
One way to do this is to choose a coefficient for \(x\) on the right side that results in a different slope than the left side. A straightforward choice would be to make the coefficient of \(x\) on the right side equal to \(-7\) (the same as the left side) but add a constant to ensure they are unequal.
Let's put \(-7\) in the blank and make the constant term on the right different. Thus, we can write it as:
\[
-7x - 12 = -7x + 5
\]
Now simplify this equation:
If we add \(7x\) to both sides, we get:
\[
-12 = 5
\]
This is a contradiction, which means the original equation has no solution.
So, the completed equation is:
\[
-7x - 12 = -7x + 5
\]
One way to do this is to choose a coefficient for \(x\) on the right side that results in a different slope than the left side. A straightforward choice would be to make the coefficient of \(x\) on the right side equal to \(-7\) (the same as the left side) but add a constant to ensure they are unequal.
Let's put \(-7\) in the blank and make the constant term on the right different. Thus, we can write it as:
\[
-7x - 12 = -7x + 5
\]
Now simplify this equation:
If we add \(7x\) to both sides, we get:
\[
-12 = 5
\]
This is a contradiction, which means the original equation has no solution.
So, the completed equation is:
\[
-7x - 12 = -7x + 5
\]
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