Let's solve the equation \(-2(x - 8) + 4x = -12\).

### Step 1: Distribute the \(-2\) on the left side.
\[
-2(x - 8) = -2x + 16
\]
So the equation becomes:
\[
-2x + 16 + 4x = -12
\]

### Step 2: Combine like terms on the left side.
\[
(-2x + 4x) + 16 = -12
\]
This simplifies to:
\[
2x + 16 = -12
\]

### Step 3: Move the constant term to the right side.
Subtract 16 from both sides:
\[
2x = -12 - 16
\]
Simplifying the right side:
\[
2x = -28
\]

### Step 4: Solve for \(x\).
Divide both sides by 2:
\[
x = -14
\]

So, the solution is \(x = -14\).

Would you like further explanation on any part of this process? Here are some related questions that could be helpful:

1. How do you solve equations involving both distribution and combining like terms?
2. What is the process for isolating a variable in an equation?
3. How do you handle negative signs when solving equations?
4. Can you provide examples of more complex linear equations?
5. How can you verify your solution to an equation?

**Tip:** After finding the solution, substitute it back into the original equation to confirm it satisfies the equation. This helps prevent errors.

Learn how to solve the linear equation -2(x-8) + 4x = -12 with a step-by-step solution. This problem involves algebraic concepts such as the distributive property. Suitable for students in Grades 7-9.

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