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 infinite solutions. The equation has infinite solutions. 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 one solution: x=−3 .

Answer 1

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

1. Distribute the 3 on the right side: \[ 3(7x - 1) = 21x - 3 \]

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

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

4. Now, we have the equation: \[ 11x = 11x - 3 \]

5. Next, let's subtract \(11x\) from both sides: \[ 11x - 11x = 11x - 3 - 11x \] \[ 0 = -3 \]

Since the equation simplifies to \(0 = -3\), which is a contradiction, this means there are no values of \(x\) that satisfy the original equation.

Thus, the conclusion is that the equation has no solution.