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

Question

6(2x+4)−24=12x

(1 point)
Responses

The equation has no solution.
The equation has no solution.

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

The equation has one solution: x=−20.
The equation has one solution: x equals negative 20 .

The equation has infinite solutions.

Answer 1

To solve the equation 6(2x+4)−24=12x, first distribute the 6 on the left side:

12x + 24 - 24 = 12x

Combine like terms:

12x = 12x

Subtract 12x from both sides:

0 = 0

Since this equation simplifies to 0 = 0, it means that x can be any real number. Therefore, the equation has infinite solutions.