Question

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

Answer 1

To create an equation that has no solution, we need to manipulate the equation such that it leads to a contradiction.

Starting with the original equation:

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

If we want to fill in a blank space to change this equation to one with no solution, we can make both sides equal to a different expression that leads to a contradiction.

Let's modify the equation like this:

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

Where \( k \) is some value we can choose. For instance, if we make the right-hand side equal to something that's impossible to equal to (-24, for example):

\[
-7x - 12 = x - 24
\]

Now, we can solve this modified equation:

\[
-7x - 12 = x - 24
\]

Rearranging it gives:

\[
-7x - x = -24 + 12 \\
-8x = -12 \\
x = \frac{12}{8} \\
x = \frac{3}{2}
\]

Thus, if you modify it to something impossible, it results in a contradiction. For example:

\[
-7x - 12 = x + 12 + (0)
\]
or similar modifications such as:

\[
-7x - 12 = x + 12 + k \text{ where } k \text{ does not equal } 0.
\]

To have an equation with no solution, one scenario would be:

Fill in the blank:

\[
-7x - 12 = x + 12 + 0
\]

will stay valid, but

\[
-7x - 12 = x + 12 + k \quad (consider k ≠ 0)
\]

will ensure that we create a contradiction in the solutions.

Thus, you can conclude filling the blank with another value or expression that negates equality or results in contradictions.