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Solution
$$5\frac{1}{2} - \left[3\frac{1}{4} + 6 - 4 \div 2\right] = \dfrac{11}{2} - [\dfrac{13}{4} + 6 - \dfrac{4}{2}]$$
$$= \dfrac{11}{2} - [\dfrac{13}{4} + 6 - 2] = \dfrac{11}{2} - [\dfrac{13}{4} + 4] = \dfrac{11}{2} - \dfrac{29}{4} = \dfrac{22-29}{4} = \dfrac{-7}{4}$$
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