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

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

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1 answer

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.