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

6(2x+4)−24=12x

(1 point)
Responses

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

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

The equation has infinite solutions.
The equation has infinite solutions.

The equation has one solution: x=0.

1 answer

To solve the equation \( 6(2x + 4) - 24 = 12x \), let's start by simplifying both sides.

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

  2. Simplify the left side: \[ 12x = 12x \]

This equation is always true for any value of \( x \) because both sides are identical. Therefore, we conclude that the equation has infinite solutions.

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