To solve the equation \( \frac{5}{3} - 2x = \frac{1}{6} \), follow these steps:
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First, isolate the term with \( x \) by moving \( \frac{5}{3} \) to the right side: \[ -2x = \frac{1}{6} - \frac{5}{3} \]
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To subtract the fractions, find a common denominator. The least common multiple of 6 and 3 is 6. Rewrite \( \frac{5}{3} \): \[ \frac{5}{3} = \frac{10}{6} \]
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Substitute this back into the equation: \[ -2x = \frac{1}{6} - \frac{10}{6} = \frac{1 - 10}{6} = \frac{-9}{6} \] which simplifies to: \[ -2x = \frac{-3}{2} \]
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To solve for \( x \), divide both sides by -2: \[ x = \frac{-3}{2} \div -2 = \frac{-3}{2} \cdot \frac{-1}{2} = \frac{3}{4} \]
Thus, the solution to the equation \( \frac{5}{3} - 2x = \frac{1}{6} \) is: \[ x = \frac{3}{4} \]
Among the response options provided, the answer is: \[ \frac{3}{4} \]