Math CentralQuandaries & Queries


Question from Natasha, a student:

Would one flip the inequality symbol in this equation: (explain why)
(-9a)/(-9) > 81
And please explain in what circumstances one would flip the inequality sign

Hi Natasha,

To solve for $a$ in this problem

\[\frac{-9a}{-9} > 81\]

you can cancel the $-9$ in the numerator with the $-9$ in the denominator to get $a > 81.$

You need to change the direction of the inequality if you multiply each side of the inequality by a negative number. Thus, for example, if your question had been to solve $-9 a > 81$ then I would multiply each side by $\frac{1}{-9}$ and the inequality becomes

\[\frac{1}{-9} \times (-9 a) < \frac{1}{-9} \times 81\]


\[a < -9.\]

I hope this helps,

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