Let's solve the equation step by step:

Given equation:
\[
-8 - x = -3(2x - 4) + 3x
\]

### Step 1: Distribute the \(-3\) on the right side
\[
-8 - x = -3 \cdot 2x + (-3) \cdot (-4) + 3x
\]
\[
-8 - x = -6x + 12 + 3x
\]

### Step 2: Combine like terms on the right side
\[
-8 - x = (-6x + 3x) + 12
\]
\[
-8 - x = -3x + 12
\]

### Step 3: Move all terms involving \(x\) to one side and constant terms to the other side
Add \(3x\) to both sides:
\[
-8 - x + 3x = 12
\]
\[
-8 + 2x = 12
\]

### Step 4: Isolate \(2x\)
Add \(8\) to both sides:
\[
2x = 12 + 8
\]
\[
2x = 20
\]

### Step 5: Solve for \(x\)
Divide both sides by \(2\):
\[
x = \frac{20}{2}
\]
\[
x = 10
\]

The solution is \(x = 10\).

Would you like more details on any of the steps? Here are some related questions:

1. How would the solution change if the equation had a different coefficient for \(x\)?
2. What happens if the constants on both sides of the equation were altered?
3. How can you check if \(x = 10\) is the correct solution?
4. How would you solve a similar equation with fractions?
5. What are common mistakes to avoid when solving equations like this?

**Tip:** Always distribute multiplication over addition or subtraction within parentheses before combining like terms.

Learn how to solve the equation -8 - x = -3(2x - 4) + 3x step-by-step with detailed explanations. This problem involves equations, distributive property, combining like terms, and isolating variables. Suitable for students in Grades 7-9.

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