Question

Complete the equation so that it has no solution.(1 point)
5x+12=___ x+9

Answer 1

To complete the equation \(5x + 12 = \_\_ x + 9\) so that it has no solution, we need to set the left-hand side equal to the right-hand side in such a way that it leads to a contradiction.

One way to do this is to make the coefficients of \(x\) in both sides different while ensuring that the constant terms make it impossible to satisfy the equation.

We can set it up as follows:

Let’s choose the coefficient of \(x\) on the right side to be equal to the coefficient of \(x\) on the left side, but then add a different constant that guarantees a contradiction.

For example, we can fill in the blank with \(5\):

So, the equation is:

\[5x + 12 = 5x + 9\]

Now, if we subtract \(5x\) from both sides, we get:

\[12 = 9\]

This statement is false, which means the equation has no solution.

Thus, the completed equation is:

\[5x + 12 = 5x + 9\]