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=0.
The equation has one solution: x equals 0 .
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 no solution.
The correct response is: The equation has one solution: x = -10.
To determine if the equation has one, none, or infinite solutions, let's solve it step-by-step:
4x = 3(x + 5) - 15
First, let's distribute 3 to both terms inside the parentheses:
4x = 3x + 15 - 15
Simplify the equation by combining like terms:
4x = 3x
Now, let's move all the terms involving x to one side of the equation:
4x - 3x = 0
Combine like terms:
x = 0
Therefore, the equation has one solution: x = 0.
The correct response is: "The equation has one solution: x = 0."