Question

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

Answer 1

To complete the equation so that it has no solution, we need to make sure that both sides simplify to contradictory statements.

Let's start with the original equation:

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

If we replace \(\_x\) with something that will make the equation impossible to satisfy, we can use a specific choice. For instance, we could set it up so that the coefficients of \(x\) are equal but the constant terms do not satisfy the equation.

Let's choose:

\[
-7x - 12 = -7x + 5
\]

Now we have:

\[
-7x - 12 = -7x + 5
\]

Subtracting \(-7x\) from both sides gives:

\[
-12 = 5
\]

This statement is clearly false, meaning that the equation has no solution.