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
.

1 answer

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.