Solve for x to determine if the equation has one, none, or infinite solutions.

Question

11x=3(7x−1)−10x (1 point)
Responses

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=−3.
The equation has one solution: x equals negative 3 .

The equation has one solution: x=−1.
The equation has one solution: x equals negative 1 .

Answer 1

To solve the equation, we can simplify it first:

11x = 3(7x - 1) - 10x

11x = 21x - 3 - 10x

11x = 11x - 3

Now, we notice that both sides of the equation have the same term (11x). This means that the equation is an identity and will be true for any value of x. Therefore, the equation has infinite solutions.

The correct response is:
The equation has infinite solutions.