+0  
 
0
13
1
avatar+2653 

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

 May 22, 2024
 #1
avatar+1837 
0

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

2 Online Users