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=0.
The equation has one solution: x equals 0 .
The equation has one solution: x=−10.
The equation has one solution: x equals negative 10 .
The equation has infinite solutions.
The equation has infinite solutions.
To solve this equation, let's simplify both sides of the equation:
4x = 3(x+5) - 15
First, distribute the 3 to both terms inside the parentheses:
4x = 3x + 15 - 15
Combine like terms:
4x = 3x
Since the 3x terms are the same on both sides of the equation, we can subtract 3x from both sides to isolate the variable:
4x - 3x = 3x - 3x
Simplifying further:
x = 0
Therefore, the equation has one solution: x = 0.