5. (2 points)

To solve the equation \(-2 - 8x = -4x - 2\) using inverse operations, we will isolate the variable \(x\) step by step. Here’s how to do it:

### Step 1: Get all \(x\) terms on one side
We can start by adding \(8x\) to both sides of the equation to eliminate the \(-8x\) from the left side.

\[
-2 - 8x + 8x = -4x - 2 + 8x
\]

This simplifies to:

\[
-2 = 4x - 2
\]

### Step 2: Get the constant terms on the other side
Next, we will add \(2\) to both sides to move the \(-2\) on the right side:

\[
-2 + 2 = 4x - 2 + 2
\]

This simplifies to:

\[
0 = 4x
\]

### Step 3: Isolate \(x\)
Next, we divide both sides by \(4\):

\[
\frac{0}{4} = \frac{4x}{4}
\]

This results in:

\[
0 = x
\]

### Final Answer
The solution to the equation \(-2 - 8x = -4x - 2\) is:

\[
x = 0
\]

You can verify by substituting \(x = 0\) back into the original equation:

\[
-2 - 8(0) = -4(0) - 2 \implies -2 = -2
\]

This confirms that the solution is correct.

Feel free to use any sketch pad or digital tool to visually represent these steps, keeping track of each transformation in the equation.