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 infinite solutions. The equation has infinite solutions. The equation has one solution: x=−10. The equation has one solution: x equals negative 10 . The equation has one solution: x=0. The equation has one solution: x equals 0 . The equation has no solution.

Answer 1

To solve for \( x \) in the equation \( 4x = 3(x + 5) - 15 \):

1. Start by distributing the \( 3 \) on the right side: \[ 4x = 3x + 15 - 15 \] This simplifies to: \[ 4x = 3x \]

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

Now, let's see if this situation indicates one, none, or infinite solutions.

Since we found one solution, \( x = 0 \), there is indeed one solution to this equation.

The appropriate response is: The equation has one solution: x = 0.