Answer:
➧x>0 & x<-8
Steps:
➧9-∣x+4∣<5
Add -9 to both sides
➧9-∣x+4∣-9<5-9
➧-∣x+4∣<-4
Replace x+4 by X ☆☆
➧-∣X∣<-4
☆☆Note:
1)∣X∣ = -X if X is negative or <0
2)∣X∣ = X if X is positive or >0
1) If X is negative no
➧-(-X)<-4
➧X<-4
➧x+4<-4
Add -4 to both sides
➧x+4-4<-4-4
➧x<-8
2) If X is positive no
➧-(X)<-4
➧-X<-4
➧-(x+4)<-4
➧-x-4<-4
Add 4 to both sides
➧-x-4+4<-4+4
➧-x<0
Multiply both side by -1 ☆☆☆
➧x>0
☆☆☆
Multiplying both sides by a negative no changes > to < and vice versa