To solve the equation \( 12y - 2x = 12 \) for one variable in terms of the other, let’s isolate \( y \).
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Start with the equation: \[ 12y - 2x = 12 \]
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Add \( 2x \) to both sides: \[ 12y = 2x + 12 \]
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Now, divide every term by \( 12 \): \[ y = \frac{2x + 12}{12} \]
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Simplify the right side: \[ y = \frac{2x}{12} + \frac{12}{12} = \frac{x}{6} + 1 \]
So, the equation can be rewritten as: \[ y = \frac{x}{6} + 1 \]
If you need to solve for \( x \) in terms of \( y \), you can do the following:
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Start with the original equation: \[ 12y - 2x = 12 \]
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Rearrange it to isolate \( x \): \[ -2x = 12 - 12y \]
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Divide by \( -2 \): \[ x = 6y - 6 \]
Thus, \( x \) can be expressed as: \[ x = 6y - 6 \]
You can use either form depending on which variable you want to express in terms of the other.