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

The equation has no solution.
The equation has no solution.

The equation has infinite solutions.

Answer 1

To solve the equation \( 6(2x+4)−24=12x \), we will simplify and isolate \( x \).

1. Distribute the 6 on the left side:

\[
6(2x) + 6(4) - 24 = 12x
\]
\[
12x + 24 - 24 = 12x
\]
\[
12x = 12x
\]

2. After simplifying, we see that both sides of the equation are equal (12x = 12x). This suggests the equation holds true for all values of x.

Therefore, the equation has infinite solutions.

The correct response is:
**The equation has infinite solutions.**