Solve for 2 to determine if the equation has one, none, or infinite solutions. 11x = 3(7x - 1) - 10x (1 point) The equation has no solution The equation has infinite solutions The equation has one solution x = - 1 The equation has one solution x = - 3

Answer 1

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

1. Distribute the 3 on the right: \[ 3(7x - 1) = 21x - 3 \] So the equation now looks like: \[ 11x = 21x - 3 - 10x \]

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

3. Next, subtract \( 11x \) from both sides: \[ 11x - 11x = 11x - 11x - 3 \] Which simplifies to: \[ 0 = -3 \]

The equation \( 0 = -3 \) is a contradiction, indicating that there are no values of \( x \) that satisfy the equation.

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