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

6(2x+4)−24=12x

A. The equation has one solution: x=0.

B. The equation has no solution.

C. The equation has one solution: x=−20.

D. The equation has infinite solutions.

1 answer

Let's solve the equation step by step:

6(2x+4) - 24 = 12x

Distribute 6 to both terms in the parentheses:

12x + 24 - 24 = 12x

The 24 and -24 cancel out:

12x = 12x

This equation is an identity because both sides are equal regardless of the value of x. Therefore, the equation has infinite solutions. The answer is D.