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

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

2. Substitute back into the equation: \[ 4x = 3x + 15 - 15 \] This simplifies to: \[ 4x = 3x \]

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

Now we check our results. The equation simplifies to a statement \( x = 0 \), which indicates that there is one solution.

Thus, the final conclusion is: The equation has one solution: x equals 0.