To solve the equation \( 4x = 5x - 12 \), you can follow these steps:
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Subtract \( 5x \) from both sides to get all the \( x \) terms on one side: \[ 4x - 5x = -12 \]
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This simplifies to: \[ -x = -12 \]
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To solve for \( x \), multiply both sides by -1: \[ x = 12 \]
Thus, the value of \( x \) is \( \boxed{12} \).