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 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 no solution.
The equation has no solution.

The equation has one solution: x=0
.
The equation has one solution: x equals 0 .
Remaining Attempts : 3
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Answer 1

Let's solve the equation step by step:

The original equation is:

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

First, distribute the 6 on the left side:

\[ 12x + 24 - 24 = 12x \]

This simplifies to:

\[ 12x = 12x \]

Now we see that both sides of the equation are equal. This means that the equation is true for all values of \( x \).

Therefore, the equation has **infinite solutions**.