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

6(2x + 4) - 24 = 12x
A. The equation has infinite solutions.
B. The equation has one solution: x = -20.
C. The equation has one solution: x = 0.
D. The equation has no solution.

1 answer

To solve the equation \( 6(2x + 4) - 24 = 12x \), we start by simplifying and rearranging the left side.

  1. Distribute \( 6 \) to both terms inside the parentheses: \[ 6 \cdot 2x + 6 \cdot 4 = 12x + 24 \] Substituting back into the equation gives: \[ 12x + 24 - 24 = 12x \]

  2. Now simplify the left side: \[ 12x + 24 - 24 = 12x \] which simplifies to: \[ 12x = 12x \]

  3. This results in an identity, meaning that the equation is true for all values of \( x \).

Since the equation simplifies to \( 12x = 12x \), we conclude that the equation has infinite solutions.

Therefore, the correct answer is: A. The equation has infinite solutions.