Question

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

3(x+2)−6=3x(1 point)

A. The equation has one solution: x=−3.

B. The equation has one solution: x=3.

C. The equation has no solution.

D. The equation has infinite solutions

Answer 1

[AI-generated answer — Bot GPT 3.5]

To determine the number of solutions for the equation, let's solve for x:

3(x+2) - 6 = 3x
3x + 6 - 6 = 3x
3x = 3x
By subtracting 3x from both sides, we get 0 = 0.
Since 0 = 0, this means that all values of x will satisfy the equation. Therefore, the equation has infinite solutions.
The correct answer is D. The equation has infinite solutions.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To solve the equation 3(x+2) - 6 = 3x, we will simplify the equation step by step:

1. Distribute the 3 on the left side of the equation:
3x + 6 - 6 = 3x

2. Simplify:
3x = 3x

3. Subtract 3x from both sides to isolate the variable:
3x - 3x = 0

4. Simplify:
0 = 0

Since we ended up with 0 = 0, this means that the equation is true for any value of x. Therefore, the equation has infinite solutions.

The correct answer is D. The equation has infinite solutions.