We will solve the equation step by step:

### Given equation:
\[
-(3x + 8) + 6 = -(7x - 9)
\]

### Step 1: Distribute the negative signs.
Distribute the negative sign on both sides:

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

### Step 2: Simplify both sides.
On the left-hand side:
\[
-3x - 8 + 6 = -3x - 2
\]
So, the equation becomes:
\[
-3x - 2 = -7x + 9
\]

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

Now, add 2 to both sides:
\[
4x = 11
\]

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

So, the solution is:
\[
x = \frac{11}{4} \quad \text{or} \quad 2.75
\]

Would you like more details on any step or have any questions?

Here are 5 related questions:
1. How would you solve if the equation involved fractions?
2. How does distributing negative signs affect an equation?
3. What is the next step if we had variables on both sides of a more complex equation?
4. How do you solve equations that involve powers of \(x\)?
5. What if the equation had decimals instead of fractions?

**Tip**: Always combine like terms first before moving terms across the equals sign to simplify equations faster.

Learn how to solve the linear equation −(3x+8)+6=−(7x−9) with a detailed step-by-step solution. This problem involves algebraic concepts such as distributing negative signs, combining like terms, and isolating variables. Suitable for students in Grades 8-10.

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