Question

Rozwiąż nierówności:

a) ||x-1|-7|>3

b) ||2x+3|-4|<1

Answer 1

a)

||x-1|-7|>3

|x-1|-7>3

|x-1|>10

x-1>10

x>11

 

x-1<-10

x<-9

 

|x-1|-7<-3

|x-1|<4

x-1<4

x<5

 

x-1>-4

x>-3

 

x∈(-∞,-9)u(-3,5)u(11,∞)

b)

||2x+3|-4|<1

|2x+3|-4<1

|2x+3|<5

2x+3<5

2x<2

x<1

 

2x+3>-5

2x>-8

x>-4

 

|2x+3|-4>-1

|2x+3|>3

2x+3>3

2x>0

x>0

 

2x+3<-3

2x<-6

x<-3

 

x∈(-4,-3)u(0,1)