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Solve the inequality x(x + 6) > 16 - x + 14 + x^2. Write your answer in interval notation.

 Aug 10, 2024
 #1
avatar+10 
+1

expand:

x^2+6x>16-x+14+x^2

cancel out x^2:

7x>30

x>30/7

in interval notation:

(30/7, ∞)

edited i made some silly mistakes

 Aug 10, 2024
edited by doeansodc  Aug 10, 2024
 #2
avatar+1897 
+1

doeansodc has the right idea, but just mae a careless error. 

He simplified it correctly to get \(x^2+6x>16-x+14+x^2 \)

 

Now, canceling out the x^2, we get

\(6x>16-x+14 \)

 

Isolating x, we have

\(7x > 30\\ x > 30/7\)

 

Thus, in interval notation, we have

\((30/7, \infty)\)

 

Thanks! :)

NotThatSmart  Aug 10, 2024
edited by NotThatSmart  Aug 10, 2024

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