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 no solution. The equation has no solution. 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 infinite solutions.

Answer 1

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

1. Distribute the \( 3 \) on the right side: \[ 3(x + 5) = 3x + 15 \] So the equation becomes: \[ 4x = 3x + 15 - 15 \]

2. Simplify the right side: \[ 4x = 3x + 0 \] This simplifies further to: \[ 4x = 3x \]

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

Since we obtained a specific value for \( x \) (i.e., \( x = 0 \)), the original equation has one solution.

Thus, the correct response is:

• The equation has one solution: \( x = 0 \).