Evaluate: \(6 - \left[\dfrac{2}{3} \div \left\{\dfrac{1}{6} + \left(\dfrac{1}{2}\times \left(1 - \dfrac{1}{3}\right)\right)\right\}\right]\)
\(\dfrac{14}{3}\)
Step 1 – Innermost bracket: \(1 - \dfrac{1}{3} = \dfrac{2}{3}\).
Step 2 – Multiply by 1/2: \(\dfrac{1}{2}\times \dfrac{2}{3} = \dfrac{1}{3}\).
Step 3 – Add 1/6: \(\dfrac{1}{6} + \dfrac{1}{3} = \dfrac{1}{2}\).
Step 4 – Divide 2/3 by 1/2: \(\dfrac{2}{3} \div \dfrac{1}{2} = \dfrac{4}{3}\).
Step 5 – Subtract from 6: \(6 - \dfrac{4}{3} = \dfrac{14}{3}\).
Hence, the correct answer is \(\dfrac{14}{3}\).
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