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

learnmgcat Aug 10, 2024

#1**+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

doeansodc Aug 10, 2024

#2**+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