Solve and Determine if the equation has one, none or infinite solutions.

Question

Solve and Determine if the equation has one, none or infinite solutions. 
-11 + x = -7x - 8(-x + 1)

explain short

GPT-4o mini · Answer

Let's solve the equation step by step:

The given equation is:

$- 11 + x = - 7 x - 8 (- x + 1)$

First, simplify the right side:

$- 8 (- x + 1) = 8 x - 8$

Now, substitute back into the equation:

$- 11 + x = - 7 x + 8 x - 8$

Combine like terms on the right side:

$- 11 + x = x - 8$

Next, subtract $x$ from both sides:

$- 11 = - 8$

This is a false statement, which means the original equation has no solutions.

The equation $- 11 + x = - 7 x - 8 (- x + 1)$ has no solutions because it leads to a contradiction.