Find all x that satisfy the inequality (2x+10)(x+3)<(3x+9)(x-8) . Express your answer in interval notation.

Guest Jul 30, 2022

#1**+2 **

Answer: \(x\in(-\infty, -3) \cup (34, \infty)\)

Solution:

Set the equations equal to find critical points:

(2x+10)(x+3)=3(x+3)(x-8)

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:

(0+10)(0+3)=3(0+3)(0-8)

This region is not shaded.

The regions around it (x<-3 and x>34) are.

Therefore, the answer in interval notation is \(x\in(-\infty, -3) \cup (34, \infty)\).

WhyamIdoingthis Jul 30, 2022