To solve the equation \( \frac{5}{3} - 2x = \frac{1}{6} \), you can follow these steps:
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Isolate the term with \(x\): \[ -2x = \frac{1}{6} - \frac{5}{3} \]
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Convert \( \frac{5}{3} \) to have a common denominator with \( \frac{1}{6} \). The common denominator of 6 and 3 is 6: \[ \frac{5}{3} = \frac{5 \times 2}{3 \times 2} = \frac{10}{6} \]
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Substitute this back into the equation: \[ -2x = \frac{1}{6} - \frac{10}{6} \] \[ -2x = -\frac{9}{6} \]
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Simplify the fraction: \[ -\frac{9}{6} = -\frac{3}{2} \]
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Now the equation is: \[ -2x = -\frac{3}{2} \]
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Divide both sides by -2 to solve for \(x\): \[ x = -\frac{3}{2} \div -2 = -\frac{3}{2} \times -\frac{1}{2} = \frac{3}{4} \]
Thus, the solution to the equation is \( \boxed{\frac{3}{4}} \).