Solve for x

Question

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

6(2x+4)−24=12x


(1 point)
Responses

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

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

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

The equation has one solution: x=−20
.

Answer 1

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

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

2. Combine like terms on the left side: \[ 12x + 0 = 12x \] This simplifies to: \[ 12x = 12x \]

Now we observe that both sides of the equation are identical. This means the equation holds true for all values of \(x\).

Hence, we conclude that the equation has infinite solutions.

The correct response is: The equation has infinite solutions.