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=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.
The equation has infinite solutions.
The equation has no solution.
The equation has one solution: x = -20.
To solve the equation 6(2x+4)−24=12x, we can start by simplifying both sides of the equation:
Distribute the 6 to the terms inside the parentheses:
12x + 24 - 24 = 12x
Now, combine like terms:
12x + 0 = 12x
This equation simplifies to:
12x = 12x
When we have an equation where both sides are equal, it means that the equation has infinite solutions. Therefore, the correct response is:
The equation has infinite solutions.