To solve the equation \( \frac{5}{3} - 2x = \frac{1}{6} \), we can follow these steps:
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Subtract \( \frac{5}{3} \) from both sides of the equation: \[ -2x = \frac{1}{6} - \frac{5}{3} \]
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To subtract the fractions, we need a common denominator. The common denominator of 6 and 3 is 6. Rewrite \( \frac{5}{3} \) with a denominator of 6: \[ \frac{5}{3} = \frac{5 \times 2}{3 \times 2} = \frac{10}{6} \]
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Now we can perform the subtraction: \[ -2x = \frac{1}{6} - \frac{10}{6} = \frac{1 - 10}{6} = \frac{-9}{6} \] Simplifying \( \frac{-9}{6} \) gives: \[ -2x = \frac{-3}{2} \]
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Now, divide both sides by -2: \[ x = \frac{-3/2}{-2} = \frac{-3}{2} \times \frac{1}{-2} = \frac{3}{4} \]
Thus, the solution to the equation is: \[ x = \frac{3}{4} \]
From the responses you provided, the correct answer is: \( \frac{3}{4} \).