To solve the equation \( 4 (8x - 1) = 2 (2x - 2) \), we will start by expanding both sides.
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Expand the left side:
\[ 4 \times (8x - 1) = 32x - 4 \] -
Expand the right side:
\[ 2 \times (2x - 2) = 4x - 4 \]
Now, we can rewrite the equation with the expansions: \[ 32x - 4 = 4x - 4 \]
Next, we will isolate the variable \( x \). Start by adding \( 4 \) to both sides to eliminate the constant term: \[ 32x - 4 + 4 = 4x - 4 + 4 \] This simplifies to: \[ 32x = 4x \]
Now, subtract \( 4x \) from both sides: \[ 32x - 4x = 4x - 4x \] This simplifies to: \[ 28x = 0 \]
Finally, divide both sides by \( 28 \): \[ x = \frac{0}{28} = 0 \]
Thus, the solution is: \[ \boxed{0} \]