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Why should we avoid multiplying each side of an inequality by a variable?

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If an inequality is multiplied by a positive value, then we can get an inequality with same direction of > or <, in other words, if an equality is of the form a>b, then it becomes
ac>bc if c>0.

If an ...

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Multiplying each side of an inequality by a variable is discussed. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.