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The equation given is:

\[
-(3x + 8) + 6 = -(7x - 9)
\]

Let's solve it step by step:

### Step 1: Distribute the negative signs on both sides
\[
-(3x + 8) = -3x - 8 \quad \text{and} \quad -(7x - 9) = -7x + 9
\]
So the equation becomes:
\[
-3x - 8 + 6 = -7x + 9
\]

### Step 2: Simplify the constants on the left side
\[
-3x - 2 = -7x + 9
\]

### Step 3: Move all terms involving \(x\) to one side and constant terms to the other side
Add \(7x\) to both sides:
\[
4x - 2 = 9
\]

### Step 4: Solve for \(x\)
Add 2 to both sides:
\[
4x = 11
\]
Divide by 4:
\[
x = \frac{11}{4}
\]

Thus, the solution is:
\[
x = \frac{11}{4}
\]

Would you like a more detailed explanation or any clarifications? Here are five related questions you might want to explore:
1. How can you verify the solution for this equation?
2. What happens if we solve a similar equation but with different coefficients?
3. How do you handle equations with more complex distributions?
4. What if the equation involved fractions from the start?
5. How do you graphically represent the solution of a linear equation?

**Tip**: When dealing with negatives in parentheses, always distribute carefully to avoid sign errors.

Learn how to solve the linear equation -(3x + 8) + 6 = -(7x - 9) using distributive properties and basic algebraic techniques. Follow the step-by-step solution to understand the process of isolating x and finding the correct answer. Ideal for students in Grades 8-10.

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