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Solve the inequality $x(x + 6) > 16 - 5x + 33.$ Write your answer in interval notation.

 May 22, 2024
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First, we have to write this in standard form by combining all like terms and moving all terms to one side. We get \(x^2+11x-49>0\)

 

Using the quadratic equation, we get \(x<\frac{-\sqrt{317}-11}{2}\quad \mathrm{or}\quad \:x>\frac{\sqrt{317}-11}{2}\)

 

Putting this into interval notation, we have \((\frac{-\sqrt{317}-11}{2}, \frac{\sqrt{317}-11}{2})\)

 

This isn't a hard problem to do. It is annoying we have square roots and an unfactorable polynomial, but not too bad in general!

 

Thanks! :)

 May 23, 2024

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