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

Question

3 (x + 2) − 6 = 3x

1. The equation has no solution.
2. The equation has one solution: x = −3.
3. The equation has one solution: x = 3.
4. The equation has infinite solutions.

Answer 1

Let's start by simplifying the left side of the equation:

3(x + 2) − 6 = 3x
3x + 6 - 6 = 3x Distribute the 3
3x = 3x Combine like terms

We have 3x on both sides of the equation, so we can simplify further by subtracting 3x from both sides:

3x - 3x = 0
0 = 0

This is true for any value of x; there are infinite solutions to the equation. Therefore, the answer is:

4. The equation has infinite solutions.