To manipulate the equation \( y = 7x - 12 \) in order to express \( x \) in terms of \( y \), follow these steps:
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Start with the original equation: \[ y = 7x - 12 \]
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Add 12 to both sides to isolate the term with \( x \): \[ y + 12 = 7x \]
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Next, divide both sides by 7 to solve for \( x \): \[ x = \frac{y + 12}{7} \]
Thus, the equation equivalent to \( y = 7x - 12 \) written in terms of \( x \) is: \[ x = \frac{y + 12}{7} \]