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 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.
The equation has infinite solutions.

The equation has no solution.

Answer 1

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

1. Distribute \( 3 \) in \( 3(x + 5) \): \[ 3(x + 5) = 3x + 15 \]

2. Substitute this back into the equation: \[ 4x = 3x + 15 - 15 \] Simplifying further gives us: \[ 4x = 3x + 0 \] Which simplifies to: \[ 4x = 3x \]

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

Now, we have found a solution \( x = 0 \).

To determine the type of solution:

• Since we ended up with a single solution for \( x \), we conclude that the equation has one solution.

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