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 no solution.
The equation has no solution.
The equation has infinite solutions.
The equation has infinite solutions.
The equation has one solution: x=−10.
To solve the equation 4x=3(x+5)-15, we can start by simplifying both sides:
4x = 3x + 15 - 15
Next, we can combine like terms:
4x = 3x
Now, we can subtract 3x from both sides:
4x - 3x = 3x - 3x
This simplifies to:
x = 0
Therefore, the equation has one solution: x = 0.
To determine if the equation 4x = 3(x + 5) - 15 has one, none, or infinite solutions, we need to solve for x.
First, distribute the 3 to (x + 5):
4x = 3x + 15 - 15
Simplify:
4x = 3x
To isolate x, subtract 3x from both sides:
4x - 3x = 0
Simplify:
x = 0
Therefore, the equation has one solution: x = 0.