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 no solution.
The equation has no solution.
The equation has infinite solutions.
The equation has infinite solutions.
The equation has one solution: x=−20.
The equation has one solution: x equals negative 20 .
The equation has one solution: x=0.
To solve the equation 6(2x+4) - 24 = 12x, we can start by simplifying the left side:
12x + 24 - 24 = 12x
Now, we can combine like terms:
12x = 12x
Notice that we have the same term on both sides of the equation. This means that the equation has infinite solutions because any value of x will satisfy the equation. Therefore, the correct response is:
The equation has infinite solutions.
To solve for x in the equation 6(2x+4)−24=12x, let's follow these steps:
1. Distribute 6 to the terms inside the parentheses:
12x + 24 - 24 = 12x
2. Combine like terms:
12x - 12x = 0
3. The equation simplifies to 0 = 0.
Since the equation simplifies to a true statement (0 = 0), this means that the equation has infinite solutions.