Question

16 Rezolvati în R a) |2x – 1| ≤ 5; inecuatiile:

b) c) 301-11 16: 2 2x + 1 3 +¹ ​

Answer 1

Explicație pas cu pas:

a)

|2x-1|<=5

-5<=2x-1<=5 |+1

-4<=2x<=6 |:2

-2<=x<=3 => x=[-2;3]

b)

|2x+1/3|<1

-1<2x+1/3<1 |×3

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

-4<2x<2 |:2

-2<x<1 => x=(-2;1)

c)

|3x-1/2-1|<=6

-6<=3x-1/2-1<=6 |×2

-12<=3x-1-2<=12 |+3

-9<=3x<=15 |:3

-3<=x<=5 => x=[-3;5]

d)

|x-x-1/2|<7

-7<x-x-1/2<7 |×2

-14<2x-x-1<14 |+1

-13<x<15 => x=(-13;15)