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Solve for x to determine if the equation has one, none, or infinite solutions. 4x=3(x+5)−15(1 point) Responses The equation has one solution: x=−10. The equation has one solution: x equals negative 10 . The equation has infinite solutions. The equation has infinite solutions. 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 .

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To solve the equation \( 4x = 3(x + 5) - 15 \), let's begin by simplifying the right side:

  1. Distribute \( 3 \) in \( 3(x + 5) \): \[ 3(x + 5) = 3x + 15 \] So the equation becomes: \[ 4x = 3x + 15 - 15 \] Simplifying further gives: \[ 4x = 3x \]

  2. Next, we'll subtract \( 3x \) from both sides: \[ 4x - 3x = 0 \] This simplifies to: \[ x = 0 \]

Since the equation resolved to \( x = 0 \), this tells us that the equation has one solution.

Thus, the correct response is: The equation has one solution: x = 0.