Let's solve the equation step by step:
The original equation is: \[ 11x = 3(7x - 1) - 10x \]
First, distribute \(3\) on the right side: \[ 11x = 3 \cdot 7x - 3 \cdot 1 - 10x \] \[ 11x = 21x - 3 - 10x \]
Now, combine like terms on the right side: \[ 11x = (21x - 10x) - 3 \] \[ 11x = 11x - 3 \]
Next, subtract \(11x\) from both sides: \[ 11x - 11x = 11x - 3 - 11x \] \[ 0 = -3 \]
The equation \(0 = -3\) is a contradiction, which means there are no solutions to the equation.
Therefore, the final answer is that the equation has none solutions.