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cross-multiplication & inequalities

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Please explain to me,What is the inherent meaning and justification of cross-multiplication as it applies to solving an inequality?

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This solution is comprised of a detailed explanation to answer what is the inherent meaning and justification of cross-multiplication as it applies to solving an inequality.

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"Cross multiplying" is synonymous with " clearing denominators" , the process by which one multiplies
an (in)equality by the product, or the least common multiple, of the denominators present.

For instance, suppose that x/y = w/z; then we can multiply both sides by the product of the denominators y and z and we obtain

(yz) (x/y) = ...

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