Let's solve the equation step by step, ensuring we've clearly isolated \(x\).
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Start with the original equation: \[ 4(x - 5) = 20 - x \]
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Distribute on the left side: \[ 4x - 20 = 20 - x \]
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To isolate \(x\), add \(x\) to both sides: \[ 4x - 20 + x = 20 - x + x \] This simplifies to: \[ 5x - 20 = 20 \]
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Next, add \(20\) to both sides to eliminate the constant on the left: \[ 5x - 20 + 20 = 20 + 20 \] This simplifies to: \[ 5x = 40 \]
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Finally, divide both sides by \(5\) to solve for \(x\): \[ x = \frac{40}{5} \] Thus, we have: \[ x = 8 \]
So the final answer is: \[ \boxed{8} \]