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 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.

Answer 1

To solve the equation \(4x = 3(x + 5) - 15\), we will first simplify the right-hand side.

1. Expand the right-hand side: \[ 3(x + 5) - 15 = 3x + 15 - 15 = 3x \]

2. Now we can rewrite the equation: \[ 4x = 3x \]

3. Next, isolate \(x\) by subtracting \(3x\) from both sides: \[ 4x - 3x = 0 \implies x = 0 \]

Since we found a single value for \(x\) (which is \(x = 0\)), we conclude that the equation has one solution.

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