We are given the equation:

\[
-5(-x - 6) = 7x - 8
\]

Let's solve it step by step:

### Step 1: Distribute the \(-5\) on the left side.
\[
-5(-x - 6) = -5(-x) - 5(-6) = 5x + 30
\]
So, the equation becomes:
\[
5x + 30 = 7x - 8
\]

### Step 2: Move all terms involving \(x\) to one side and constant terms to the other.
Subtract \(5x\) from both sides:
\[
5x + 30 - 5x = 7x - 8 - 5x
\]
This simplifies to:
\[
30 = 2x - 8
\]

### Step 3: Isolate \(x\).
Add 8 to both sides:
\[
30 + 8 = 2x
\]
\[
38 = 2x
\]

Now, divide both sides by 2:
\[
x = \frac{38}{2} = 19
\]

### Final Answer:
\[
x = 19
\]

Would you like a more detailed explanation on any step?

Here are 5 related questions to deepen your understanding:
1. How do you distribute negative signs properly when solving equations?
2. What are the steps to isolate variables in linear equations?
3. How do you check your solution in an algebraic equation?
4. Can we solve this equation using a graphical method?
5. What happens if we add or subtract terms with variables on both sides?

**Tip:** Always check your solution by substituting the value of \(x\) back into the original equation to ensure it satisfies both sides.

Learn how to solve the linear equation -5(-x - 6) = 7x - 8 step-by-step, utilizing the distributive property and techniques for isolating variables. This problem is ideal for students in Grades 7-9 learning algebraic concepts.

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