Question

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

3(x+2)−6=3x

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

B. The equation has infinite solutions.

C. The equation has no solution.

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

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve the equation, we distribute the 3 to both terms inside the parentheses:

3x + 6 - 6 = 3x

The +6 and -6 cancel out:

3x = 3x

Since the term 3x is the same on both sides of the equation, we can subtract 3x from both sides:

3x - 3x = 3x - 3x

0 = 0

The equation 0 = 0 is true for all values of x, which means there are an infinite number of solutions.

Therefore, the answer is B. The equation has infinite solutions.

Answer 2

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

To solve the equation, we can start by distributing the 3 to both terms in the parentheses:

3(x+2) - 6 = 3x

3x + 6 - 6 = 3x

Simplifying the equation:

3x = 3x

The equation 3x = 3x means that the two sides of the equation are equal for any value of x. This implies that the equation has infinite solutions.

Therefore, the correct answer is:

B. The equation has infinite solutions.