Question

Polynomial Inequalities:

8) x^2 + 7x < -12

show number line test and answer in interval notation

Answer 1

$x^2+7x<-12\\ \Rightarrow x^2+7x+12<0\\ \Rightarrow x^2+3x+4x+12<0\\ \Rightarrow x(x+3)+4(x+3)<0\\ \Rightarrow (x+3)(x+4)<0\\$

$\therefore x\in(-4,-3)$