Solve for x to determine if the equation has one, none, or infinite solutions.
11x=3(7x−1)−10x (1 point)
Responses
The equation has no solution.
The equation has no solution.
The equation has one solution: x=−1.
The equation has one solution: x equals negative 1 .
The equation has one solution: x=−3.
The equation has one solution: x equals negative 3 .
The equation has infinite solutions.
To solve the equation, we first distribute the 3 on the right side of the equation:
11x = 21x - 3 - 10x
Next, we combine the x terms on the right side:
11x = 11x - 3
Since the variable terms cancel out, we are left with:
0 = -3
This equation is not possible, as 0 cannot equal -3. Therefore, the equation has no solution.
The correct response is:
The equation has no solution.
To solve the equation 11x = 3(7x-1) - 10x, we can start by simplifying both sides of the equation:
On the right side of the equation, we distribute the 3 to both terms inside the parentheses:
11x = 21x - 3 - 10x
Next, we can combine like terms on the right side of the equation:
11x = 11x - 3
Now, we can subtract 11x from both sides of the equation to isolate the constant term:
0 = -3
Since 0 is not equal to -3, we can conclude that the equation has no solution.
To solve the equation 11x=3(7x−1)−10x and determine if it has one, none, or infinite solutions, we need to simplify and solve for x.
First, distribute the 3 to the terms inside the parentheses:
11x = 21x - 3 - 10x
Combine the like terms by subtracting 21x and -10x from both sides:
11x - 21x = -3 - 10x
-10x = -3 - 10x
Now, add 10x to both sides to isolate the constant term:
-10x + 10x = -3 - 10x + 10x
0 = -3
We obtained 0 = -3, which is a contradiction. This means that the equation has no solution.
Therefore, the correct response is: "The equation has no solution."