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What Is The Inherent Meaning And Justification Of Cross Multiplication As It Applies To Solving An Inequality In Algebra?

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Oddman answered
"Cross multiplication" is effectively multiplication by the product of the denominators on either side of the relation symbol (equality, inequality). It is a method of taking advantage of the multiplication principle, which says that multiplication of the relation by a constant does not change the values of the variables required to satisfy that relation.  When the relation is an inequality, the multiplication principle only holds for multiplication by positive constants. If the denominators are negative or contain variables, certain restrictions apply to the result and/or the inequality may need to be reversed under some conditions.  Example   2/3 > (3/4)x   Multiplying by 3*4=12 looks a lot like "cross multiplication."   2*4 > 3*3x   6 > 9x    (carry out the multiplication)   6/9 > x    (solve for x)

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