Let's solve the equation \(- (6m + 8) = 4(17 - m)\).

### Step 1: Distribute the negative sign on the left side
\[
-(6m) - 8 = -6m - 8
\]
So the equation becomes:
\[
-6m - 8 = 4(17 - m)
\]

### Step 2: Distribute the 4 on the right side
\[
-6m - 8 = 4 \times 17 - 4 \times m
\]
\[
-6m - 8 = 68 - 4m
\]

### Step 3: Add \(6m\) to both sides
\[
-8 = 68 + 2m
\]

### Step 4: Subtract 68 from both sides
\[
-8 - 68 = 2m
\]
\[
-76 = 2m
\]

### Step 5: Divide both sides by 2
\[
m = \frac{-76}{2}
\]
\[
m = -38
\]

So, the solution is \(m = -38\).

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

Here are 5 related questions to consider:

1. How would you solve the equation \(-2(3x + 5) = 5(10 - x)\)?
2. What if the equation was \(-(6m + 8) = 5(17 - m)\)? How would the solution change?
3. Can you solve \(-3(2x - 7) = 4(x + 5)\)?
4. How would you check if \(m = -38\) is the correct solution?
5. What if the negative sign was on the other side, like \(6m + 8 = -(4(17 - m))\)?

**Tip:** When solving equations involving distribution, be careful with negative signs—they can change the direction of the terms inside the parentheses.

Learn how to solve equations involving the distributive property with a step-by-step guide. This problem involves distributing on both sides of the equation and simplifying terms. Suitable for high school students.

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