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

Let's solve the equation step by step:

Given equation: \[ 6(2x + 4) - 24 = 12x \]

First, distribute the 6 on the left side: \[ 12x + 24 - 24 = 12x \]

Now, simplify the left side: \[ 12x = 12x \]

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

Final answer: The equation has infinite solutions.