Let's solve the equation \( x + 1 = -5 - (x + 6) + 8x \).

### Step 1: Simplify both sides
On the right side, distribute the negative sign over the parentheses:
\[
x + 1 = -5 - x - 6 + 8x
\]
Now, combine like terms on the right side:
\[
x + 1 = -11 + 7x
\]

### Step 2: Move all terms involving \(x\) to one side
Subtract \(x\) from both sides to move the \(x\)-terms together:
\[
1 = -11 + 6x
\]

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

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

The solution is \( x = 2 \).

Would you like more details on any part of the solution or have any questions?

Here are 5 questions to expand on this:

1. What are like terms, and how do you identify them in an equation?
2. How do you distribute negative signs in expressions?
3. What are common strategies for isolating variables in algebraic equations?
4. How can you check if your solution to an equation is correct?
5. How would the solution change if a different constant was added to both sides?

**Tip:** Always double-check your solution by substituting the value of \(x\) back into the original equation.

Learn how to solve the linear equation x + 1 = -5 - (x + 6) + 8x using key algebraic concepts such as the distributive property and combining like terms. This problem is suitable for students in Grades 8-10, with a step-by-step breakdown of isolating the variable and solving for x.

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