Question

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 no solution.
The equation has no solution.

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

The equation has infinite solutions.

Answer 1

Let's solve the equation step by step:

Starting with the equation:
\[ 6(2x + 4) - 24 = 12x \]

First, we will distribute the 6 on the left side:
\[ 12x + 24 - 24 = 12x \]

Simplifying the left side:
\[ 12x = 12x \]

At this point, we see that both sides of the equation are identical. This implies that the equation is true for all values of \( x \).

Thus, the equation has infinite solutions.

So, the correct response is:
**The equation has infinite solutions.**