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

Question

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

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.