Question

First, let’s try to isolate the variable x, or get x alone on one side of the equation. One of the x terms is inside the parentheses on the right. So, let’s start by getting rid of the parentheses to make this equation easier to work with. One way to do this is to distribute the 3 to the x and to the 3. You can think of this as (3·x)−(3·3). Rewrite the right side.
3x – 12
=
3(x − 3)

3x – 12
=
−

Answer 1

To rewrite the right side of the equation \( 3(x - 3) \), you will distribute the 3 to both terms inside the parentheses:

\[
3(x - 3) = 3x - 9
\]

Thus, the equation becomes:

\[
3x - 12 = 3x - 9
\]

Next, you can isolate the variable \( x \) by eliminating \( 3x \) from both sides:

\[
3x - 12 - 3x = 3x - 9 - 3x
\]

This simplifies to:

\[
-12 = -9
\]

Since this statement is not true, it implies there are no solutions to the original equation. Hence, the variables cancel each other out and you end up with a contradiction. There are infinitely many \( x \) values for which the left side equals the right side, as both sides were equivalent before the contradiction occurred.