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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 no solution.
The equation has no solution.

The equation has infinite solutions.
The equation has infinite solutions.

The equation has one solution: x=0
.
The equation has one solution: x equals 0 .

The equation has one solution: x=−20
.

1 answer

Let's solve the equation step by step:

  1. Start with the original equation: \[ 6(2x + 4) - 24 = 12x \]

  2. Distribute \(6\) on the left-hand side: \[ 12x + 24 - 24 = 12x \]

  3. Simplify the left-hand side: \[ 12x = 12x \]

Now, this equation \(12x = 12x\) is true for all values of \(x\). Since both sides are identical, it indicates that the equation holds true regardless of the value of \(x\).

Therefore, the conclusion is:

The equation has infinite solutions.