To solve the equation \( \frac{5}{3} - 2x = \frac{1}{6} \), follow these steps:
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Subtract \( \frac{5}{3} \) from both sides: \[ -2x = \frac{1}{6} - \frac{5}{3} \]
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To combine the right-hand side, we need a common denominator. The common denominator for 6 and 3 is 6. Convert \( \frac{5}{3} \) to sixths: \[ \frac{5}{3} = \frac{10}{6} \]
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Now subtract: \[ -2x = \frac{1}{6} - \frac{10}{6} = \frac{1 - 10}{6} = \frac{-9}{6} \]
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Simplify \( \frac{-9}{6} \) to \( \frac{-3}{2} \): \[ -2x = -\frac{3}{2} \]
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Divide both sides by \(-2\): \[ x = \frac{-\frac{3}{2}}{-2} = \frac{3}{4} \]
Thus, the solution to the equation \( \frac{5}{3} - 2x = \frac{1}{6} \) is \( \frac{3}{4} \).
The correct response is: \[ \frac{3}{4} \]