Question

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

explain short

Answer 1

Let's solve the equation step by step:

The given equation is:

\[
-11 + x = -7x - 8(-x + 1)
\]

First, simplify the right side:

\[
-8(-x + 1) = 8x - 8
\]

Now, substitute back into the equation:

\[
-11 + x = -7x + 8x - 8
\]

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**.

### Summary:
The equation \( -11 + x = -7x - 8(-x + 1) \) has **no solutions** because it leads to a contradiction.