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We are given the equation:

\[
x + 1 = -5 - (x + 6) + 8x
\]

Let's solve for \(x\) step by step.

### Step 1: Distribute the negative sign inside the parentheses.
\[
x + 1 = -5 - x - 6 + 8x
\]
Simplify the right-hand side:
\[
x + 1 = -11 + 7x
\]

### Step 2: Move all terms involving \(x\) to one side of the equation and constant terms to the other side.
Subtract \(x\) from both sides:
\[
1 = -11 + 6x
\]

### Step 3: Isolate the \(x\)-term.
Add 11 to both sides:
\[
12 = 6x
\]

### Step 4: Solve for \(x\).
Divide both sides by 6:
\[
x = 2
\]

### Final Answer:
\[
x = 2
\]

Would you like a more detailed explanation of any steps?

Here are 5 related questions:
1. How would the equation change if we added a coefficient to \(x\) on both sides?
2. What happens if you multiply the whole equation by a constant?
3. How can we verify the solution by plugging \(x = 2\) back into the original equation?
4. What methods could we use if the equation were quadratic instead of linear?
5. How do negative signs affect the order of operations in equations like this?

**Tip:** Always double-check your solution by substituting it back into the original equation to ensure correctness!

Learn how to solve the linear equation x + 1 = -5 - (x + 6) + 8x step by step, covering key algebraic concepts like distribution, combining like terms, and solving for x. Suitable for students in Grades 8-10.

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