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=−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 infinite solutions.
The correct response is: The equation has one solution: x=-10.
To solve for x, we first distribute the 3 and -15 to get:
4x = 3x + 15 - 15
Simplifying further:
4x = 3x
We then subtract 3x from both sides:
x = -10
Therefore, the equation has one solution, x = -10.
4x=3(x+5)−15(1 point)
4 x - 3 x = 15 - 15
x = 0
Period.
To determine the number of solutions, we need to simplify the equation and see if there is a variable left on both sides or if the equation is true for all values of x.
Starting with the given equation:
4x = 3(x + 5) - 15
First, distribute the 3:
4x = 3x + 15 - 15
Simplify:
4x = 3x
Now, subtract 3x from both sides:
4x - 3x = 3x - 3x
x = 0
Since we have found a specific value for x, the equation has one solution: x = 0.
To solve for x in the equation 4x = 3(x + 5) - 15, we can begin by simplifying the right side of the equation:
4x = 3x + 15 - 15
Next, we can combine like terms on the right side:
4x = 3x
To isolate x, we can subtract 3x from both sides of the equation:
4x - 3x = 3x - 3x
This simplifies to:
x = 0
Therefore, the equation has one solution: x = 0.