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 no solution.
The equation has no solution.

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.

Answer 1

To solve for x, first distribute the 6 on the left side of the equation:

12x + 24 - 24 = 12x
12x = 12x

Subtract 12x from both sides:
12x - 12x = 0
0 = 0

Since the equation simplifies to 0 = 0, this means that the equation has infinite solutions.