Question

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.

Answer 1

[AI-generated answer — Bot GPT 3.5]

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.

Answer 2

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

To solve the equation 6(2x + 4) - 24 = 12x, we can start by expanding the brackets:

12x + 24 - 24 = 12x

Simplifying further, we get:

12x = 12x

This equation shows that both sides are equal to each other, regardless of the value of x. Therefore, the equation has infinitely many solutions.

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