To solve the equation \( \frac{5}{3} - 2x = \frac{1}{6} \), we can follow these steps:
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Isolate the term containing \( x \): \[ -2x = \frac{1}{6} - \frac{5}{3} \]
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Convert \( \frac{5}{3} \) to have a common denominator with \( \frac{1}{6} \): \[ \frac{5}{3} = \frac{5 \times 2}{3 \times 2} = \frac{10}{6} \] So, the equation becomes: \[ -2x = \frac{1}{6} - \frac{10}{6} \] \[ -2x = \frac{1 - 10}{6} = \frac{-9}{6} \]
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Simplify the right side: \[ -2x = \frac{-3}{2} \]
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Divide both sides by -2: \[ x = \frac{-3/2}{-2} = \frac{-3}{-4} = \frac{3}{4} \]
Thus, the solution to the equation \( \frac{5}{3} - 2x = \frac{1}{6} \) is: \[ \boxed{\frac{3}{4}} \]