Solve for x to determine if the equation has one, none, or infinite solutions. 4x=3(x+5)−15
A. the equation has infinite solutions
B. the equation has one solution: x = -10
C. the equation has no solution
D. the equation has one solution: x = 10
To solve the equation, we first distribute on the right side:
4x = 3x + 15 - 15
This simplifies to:
4x = 3x
Next, we subtract 3x from both sides:
4x - 3x = 3x - 3x
This simplifies to:
x = 0
So the solution to the equation is x = 0. Therefore, there is only one solution to the equation.
The correct answer is:
D. the equation has one solution: x = 0