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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)ResponsesThe equation has one solution: x=−10.The equation has one solution: x equals negative 10 .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 .The equation has infinite solutions.The equation has infinite solutions.

1 answer

Let's solve the equation \( 4x = 3(x + 5) - 15 \).

  1. Distribute the \( 3 \) on the right side: \[ 4x = 3x + 15 - 15 \]

  2. Simplify the right side: \[ 4x = 3x + 0 \] \[ 4x = 3x \]

  3. Subtract \( 3x \) from both sides: \[ 4x - 3x = 0 \] \[ x = 0 \]

The equation has one solution: \( x = 0 \).

Therefore, the correct response is: The equation has one solution: x equals 0.