To move all the variables to one side of the equation \(3n + 46 = 1 + 8n\), you can subtract \(8n\) from both sides and subtract \(46\) from both sides:
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Start with: \[ 3n + 46 = 1 + 8n \]
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Subtract \(8n\) from both sides: \[ 3n - 8n + 46 = 1 \]
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This simplifies to: \[ -5n + 46 = 1 \]
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Now, subtract \(46\) from both sides: \[ -5n + 46 - 46 = 1 - 46 \]
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This simplifies to: \[ -5n = -45 \]
Now the equation with all variables on one side is: \[ -5n + 45 = 0 \]
or you can also write it as: \[ 5n - 45 = 0 \] Either form effectively isolates the variable on one side.