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Solve for x to determine if the equation has one, none, or infinite solutions

3(x+2)-6=3x
the equation has one solution: x=3
The equation has one solution: x= -3
The equation has infinite solutions.
The equation has no solution.

1 answer

Let's solve the equation step-by-step:

The equation is:

\[ 3(x + 2) - 6 = 3x \]

  1. Distribute the 3 on the left side:

\[ 3x + 6 - 6 = 3x \]

  1. Simplify the left side:

\[ 3x = 3x \]

Now, both sides of the equation are equal, which means that the equation is true for all values of \( x \). Therefore, this equation has infinite solutions.

So the correct conclusion is:

The equation has infinite solutions.