Solve for x to determine if the equation has one, none, or infinite solutions.

Question

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 infinite solutions.
The equation has infinite solutions.

The equation has one solution: x=−10.

Answer 1

To solve the equation \( 4x = 3(x + 5) - 15 \), we will start by simplifying the right side.

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

2. Now, we have the equation: \[ 4x = 3x \]

3. Next, we will subtract \( 3x \) from both sides: \[ 4x - 3x = 0 \] This simplifies to: \[ x = 0 \]

Now we check the conclusions:

• The equation \( 4x = 3(x + 5) - 15 \) simplifies to \( 4x = 3x \), which leads us to \( x = 0 \).
• This means there is one solution.

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