Find all x that satisfy the inequality (2x+10)(x+3)<(3x+9)(x-8) . Express your answer in interval notation.
Answer: \(x\in(-\infty, -3) \cup (34, \infty)\)
Set the equations equal to find critical points:
x=-3 is a critical point, as is x=34.
If this inequality were to be graphed on a number line, it would result in a striped pattern. You can test the middle region (I will test -3
Testing for 0:
This region is not shaded.
The regions around it (x<-3 and x>34) are.
Therefore, the answer in interval notation is \(x\in(-\infty, -3) \cup (34, \infty)\).