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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 no solution.
The equation has no solution.

The equation has infinite solutions.

1 answer

To solve the equation \( 11x = 3(7x - 1) - 10x \), let's first simplify the right side.

  1. Distributing \( 3 \) into \( (7x - 1) \): \[ 3(7x - 1) = 21x - 3 \]

  2. Now substitute back into the equation: \[ 11x = 21x - 3 - 10x \]

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

  4. To isolate the variable, subtract \( 11x \) from both sides: \[ 11x - 11x = 11x - 11x - 3 \] \[ 0 = -3 \]

This statement \( 0 = -3 \) is always false, which means there are no solutions to the equation.

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