To solve the equation \( 3(2x - 1) + \frac{1}{2}(4x - 2) + 2 = 0 \), let’s start by simplifying the equation step by step.
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Distributing the terms:
- The expression \( 3(2x - 1) \) becomes \( 6x - 3 \).
- The expression \( \frac{1}{2}(4x - 2) \) becomes \( 2x - 1 \).
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Substitute these into the equation: \[ 6x - 3 + 2x - 1 + 2 = 0 \]
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Combine like terms: \[ (6x + 2x) + (-3 - 1 + 2) = 0 \] This simplifies to: \[ 8x - 2 = 0 \]
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Now, solve for \( x \): \[ 8x = 2 \] \[ x = \frac{2}{8} = \frac{1}{4} \]
Thus, the solution to the equation \( 3(2x - 1) + \frac{1}{2}(4x - 2) + 2 = 0 \) is: \[ \boxed{\frac{1}{4}} \]