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One important difference between solving equations and solving inequalities is that when you multiply or divide by a negative number, then the direction of the inequality must be reversed, i.e. "less than" becomes "greater than", and "less than or equal to" becomes "greater than or equal to".

Actually, from a purist's sense, the reversal rule also applies with equations. Its just that the reversal of "equals" is still "equals". The same goes for "not equal to".

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Q: What is one important difference between solving equations and solving inequalities?
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