Answer:
[tex]\large\boxed{-5\leq k<4}[/tex]
Step-by-step explanation:
[tex]5+7k\geq-30\ \wedge\ -4k+4>20\\\\5+7k\geq-30\qquad\text{subtract 5 from both sides}\\7k\geq-35\qquad\text{divide both sides by 7}\\\boxed{k\geq-5}\\\\-4k+4>20\qquad\text{subtract 4 from both sides}\\-4k>16\qquad\text{change the signs}\\4k<-16\qquad\text{divide both ides by 4}\\\boxed{k<-4}\\\\Finally:\\\\-5\leq k<-4[/tex]
