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 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.
To solve the equation 6(2x+4)−24=12x, we will first distribute the 6 to the terms inside the parentheses:
12x + 24 - 24 = 12x
Next, we can combine like terms:
12x = 12x
We can see that both sides of the equation are equal, so no matter what value we substitute for x, the equation will always be true. Therefore, the equation has infinite solutions.
Answer: The equation has infinite solutions.
To determine if the equation 6(2x+4)−24=12x has one, none, or infinite solutions, we can begin by simplifying the equation.
First, distribute 6 to both terms inside the parentheses:
12x + 24 - 24 = 12x
Next, combine like terms:
12x + 0 = 12x
We notice that the variable x appears on both sides of the equation. Therefore, we have an infinite number of solutions.
Therefore, the correct answer is: The equation has infinite solutions.