To solve the equation \(-2 - 8x = -4x - 2\) using inverse operations, we will isolate the variable \(x\) step by step. Hereโs 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.