Question

Complete the equation so that it has no solution.
−7x − 12 = _____x + 12

Answer 1

To create an equation with no solution, we can set both sides to be parallel lines that will never intersect.

To do that, we need the coefficients of \( x \) on both sides to be equal but the constant terms to be different. Let's rewrite the left side of the equation:

\[
-7x - 12 = kx + 12
\]

To ensure there's no solution, we can choose \( k \) such that it equals -7 (the coefficient of \( x \) on the left side). However, we will make the constant terms different.

Let's get \( k = -7 \):

\[
-7x - 12 = -7x + 12
\]

Now, we can see that the left-hand side and the right-hand side have the same \( x \) coefficient (-7), but their constant terms are different (-12 on the left side and +12 on the right side). This results in:

\[
-12 \neq 12
\]

Thus, the equation \( -7x - 12 = -7x + 12 \) has no solution.

So you can fill in the blank with \(-7\):

\[
-7x - 12 = -7x + 12
\]