To solve the equation \( 11x = 3(7x - 1) - 10x \), we will first simplify the right side of the equation.
Starting with the right side: \[ 3(7x - 1) - 10x \]
Distributing \( 3 \): \[ 3 \cdot 7x - 3 \cdot 1 - 10x = 21x - 3 - 10x \]
Now, combine like terms: \[ 21x - 10x - 3 = (21x - 10x) - 3 = 11x - 3 \]
Now the original equation is: \[ 11x = 11x - 3 \]
Next, subtract \( 11x \) from both sides: \[ 11x - 11x = 11x - 3 - 11x \] \[ 0 = -3 \]
This statement \( 0 = -3 \) is a contradiction, meaning that there are no values of \( x \) that satisfy the original equation.
Thus, the solution is that there is no solution.