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