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 one solution: x=−20 . The equation has one solution: x equals negative 20 . 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 .
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To solve the equation \( 6(2x + 4) - 24 = 12x \), we will first simplify the left-hand side.
Distribute \( 6 \): \[ 6(2x + 4) = 12x + 24 \] Therefore, the equation becomes: \[ 12x + 24 - 24 = 12x \] Simplifying it further, we have: \[ 12x = 12x \]
This equation, \( 12x = 12x \), is true for any value of \( x \). This means that the equation has infinite solutions.
Thus, the answer is: The equation has infinite solutions.
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