To solve the equation:

\[
-8x - 8 = -5x + 13
\]

We aim to isolate \(x\). Follow these steps:

### Step 1: Add \(8x\) to both sides to get rid of the \(-8x\) on the left side:
\[
-8x - 8 + 8x = -5x + 13 + 8x
\]
This simplifies to:
\[
-8 = 3x + 13
\]

### Step 2: Subtract 13 from both sides to move the constant term from the right side:
\[
-8 - 13 = 3x + 13 - 13
\]
This simplifies to:
\[
-21 = 3x
\]

### Step 3: Divide both sides by 3 to solve for \(x\):
\[
x = \frac{-21}{3}
\]
\[
x = -7
\]

So, the solution is:
\[
x = -7
\]

Would you like any more details or explanations on this solution?

Here are 5 related questions:
1. How do you solve an equation with variables on both sides?
2. What happens when both sides of the equation have the same variable term?
3. Can you apply the same process to solve quadratic equations?
4. What are the key differences between solving linear and quadratic equations?
5. How do you check if a solution to an equation is correct?

**Tip:** Always double-check your solution by plugging it back into the original equation to verify it works.

Learn how to solve the linear equation -8x - 8 = -5x + 13 with a step-by-step solution. This problem involves isolating the variable x, using algebraic operations, and applying key algebraic concepts. Suitable for students in Grades 6-8.

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