Solve for x to determine if the equation has one, none, or infinite solutions.

Question

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 infinite solutions.
The equation has infinite solutions.

The equation has one solution: x=−20.
The equation has one solution: x equals negative 20 .
Skip to navigation

Answer 1

To solve for x, we can start by distributing the 6 to the terms inside the parentheses:

12x + 24 - 24 = 12x

Next, we can simplify the equation:

12x + 0 = 12x

Since the x term is the same on both sides of the equation, it cancels out:

0 = 0

The equation has infinite solutions, since any value of x will satisfy the equation.