Given, x2+5x+6≥0 and x2+3x−4<0 ⇒ x2+2x+3x+6≥0 and x2+4x−x−4<0 ⇒ x(x+2)+3(x+2)≥0 andx(x+4)−1(x+4)<0 ⇒ (x+2)(x+3)≥0 and (x+4)(x−1)<0
⇒x∈(−∞,−3]∪[−2,∞) and x∈(−4,1) Common condition is x∈(−4,−3]∪[−2,1)