Polynomials Inequalities

Question

Show number line and answer in interval notation

8) x² + 7x < -12

Answer 1

x² + 7x + 12 < 0

(x + 3(x + 4) < 0

(x+3)(x+4) = 0 when x = -3 or -4

When x<-4, x+3 and x+4 are both negative. So (x+3)(x+4) > 0

When -4<x<-3, x+3 is negative and x+4 is positive. So, (x+3)(x+4) < 0

When x>-3, x+3 and x+4 are both positive. So, (x+3)(x+4) > 0

Solution set for the inequality (x+3)(x+4) < 0 is the interval (-4, -3).