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

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.

Answer 1

Let's solve the equation \( 11x = 3(7x - 1) - 10x \).

1. Start by distributing on the right side: \[ 11x = 3(7x) - 3(1) - 10x \] \[ 11x = 21x - 3 - 10x \]

2. Combine like terms on the right side: \[ 11x = 21x - 10x - 3 \] \[ 11x = 11x - 3 \]

3. Now, subtract \( 11x \) from both sides: \[ 11x - 11x = 11x - 11x - 3 \] \[ 0 = -3 \]

Since \( 0 = -3 \) is a contradiction, this means there are no solutions to the equation.

Therefore, the correct response is: The equation has no solution.