The most appropriate method for separating an insoluble solid from a soluble solid is:
Mixing the mixture with water, filtering out the insoluble solid, and then evaporating the water to isolate the soluble solid.
Here's why the other options are less suitable:
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Melting the mixture and then using a filter to separate out the soluble solid: This method would not be effective because melting does not separate solids based on solubility; it might also damage the soluble solid.
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Melting the mixture, mixing it with water, and then using a magnet to separate out the insoluble solid: This assumes the insoluble solid is magnetic, which may not be the case. Additionally, melting the mixture before adding water is not a standard separation method.
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Mixing the mixture with water and then using chromatography to separate the two dissolved solids: Chromatography is used for separating mixtures of soluble substances, but it is not applicable for separating an insoluble solid from a soluble one.
Thus, the correct and most feasible method is the last option.