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 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 one solution: x=−10
.
The equation has one solution: x equals negative 10 .

The equation has infinite solutions.

1 answer

Let's solve the equation step by step.

The given equation is: \[ 4x = 3(x + 5) - 15 \]

First, distribute the \(3\) on the right side: \[ 4x = 3x + 15 - 15 \]

This simplifies to: \[ 4x = 3x \]

Next, we can subtract \(3x\) from both sides: \[ 4x - 3x = 0 \] \[ x = 0 \]

Now we check whether this solution is valid.

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

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