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 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.
The equation has infinite solutions.

The equation has no solution

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
10 days ago

To solve the equation \( 11x = 3(7x - 1) - 10x \), let's simplify it step by step.

  1. Distributing \( 3 \) on the right side: \[ 3(7x - 1) = 21x - 3 \] So, the equation now reads: \[ 11x = 21x - 3 - 10x \]

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

  3. To isolate \( x \), subtract \( 11x \) from both sides: \[ 11x - 11x = 11x - 11x - 3 \] This results in: \[ 0 = -3 \]

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

Therefore, the answer is: The equation has no solution.