Solve for x to determine if the equation has one, none, or infinite solutions. 6 (2x+4)−24=12x

Question

The equation has one solution: x=−20.

The equation has infinite solutions.

The equation has one solution: x=0.

The equation has no solution.

Answer 1

To solve the equation \( 6 (2x + 4) - 24 = 12x \), we will start by simplifying it step by step.

1. Distribute the 6 on the left side: \[ 6 \times (2x) + 6 \times 4 - 24 = 12x \] which simplifies to: \[ 12x + 24 - 24 = 12x \]

2. This further simplifies to: \[ 12x = 12x \]

Now, we see that both sides of the equation are identical. This indicates that the equation is valid for any value of \( x \).

Since the equation simplifies to a statement that is always true, we conclude that there are infinite solutions for this equation.

Thus, the correct answer is: The equation has infinite solutions.