Fractions, inequalities, and cross-multiplication
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When we have two fractions on either sides of an equality or inequality symbol, we can multiply the numerator on the right hand side (RHS) with the denominator of the left hand side (LHS) and the numerator of LHS with denominator of RHS. The process of multiplying across the symbol and down is referred to as cross-multiplication. Of course, when we have only one fraction on one side, we multiply only one side. The basic idea is to eliminate fractions.
a/b = c/d implies a*d = b*c
x/y = z implies x = y*z
With examples, discuss how cross-multiplication works in the context of inequalities
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Solution Summary
The solution explains how to solve an inequality involving fractions in a general way, and using specific examples.
Solution Preview
Cross multiplication works the same in inequalities as it does in equalities. I'll explain how to cross-multiply in a general sense (using the letters a-d like in your equality example), and I'll show some examples using numbers.
Start off with the inequality a/b < c/d (everything we're doing with < holds true for >)
Multiply both sides by b: a < bc/d
Multiply both ...
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