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.
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