Question

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 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.

Answer 1

To solve the equation \( 4x = 3(x + 5) - 15 \), we will simplify and solve for \( x \).

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 of the equation: \[ 4x - 3x = 0 \] This leads to: \[ x = 0 \]

The solution \( x = 0 \) indicates that there is one solution.

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