Let's solve the equation step by step:
The given equation is: \[ 4x = 3(x + 5) - 15 \]
First, simplify the right side of the equation: \[ 3(x + 5) = 3x + 15 \] So the equation becomes: \[ 4x = 3x + 15 - 15 \] This simplifies to: \[ 4x = 3x + 0 \] Thus, we can simplify further: \[ 4x = 3x \]
Next, subtract \(3x\) from both sides: \[ 4x - 3x = 0 \] \[ x = 0 \]
Now, we check the nature of solutions. We found that: \[ x = 0 \]
The equation has one solution.
Thus, the correct response is: The equation has one solution: x=0.