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

 Aug 12, 2024
 #1
avatar+1918 
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First, let's distribute in x on the right hand side of the equation. We get

\(x^2+6x > 16-x+14+x^2\)

 

Now, let's move all terms to one side and combine all like terms. The x^2 cancels out, which simplifies the problem for us. We get the inequality

\(7x-30>0\)

 

Now, we isolate x. We find that

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

 

In interval notation, this is

\((\frac{30}{7}, \infty)\)

 

Thanks! :)

 

*1600 points!

 Aug 12, 2024
edited by NotThatSmart  Aug 12, 2024
edited by NotThatSmart  Aug 12, 2024

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