Question

Va rog ajutati-ma! Solutia inecuatiei |x-1|(|2x-1|-5)<0, x apartine Z* este egala cu ...

Answer 1

|x-1|(|2x-1|-5)<0, x∈ Z*

|a| ≥ 0, ∀ a ∈ IR
       ↓
|x-1| ≥ 0
|x-1|(|2x-1|-5)<0 
⇒ |2x-1|-5<0
⇒ |2x-1| < 5 ⇔ -5 < 2x-1 < 5 | + 1
                        -4 < 2x    < 6 | :2
                        -2 < x      < 3
                             x ∈ Z* ⇒  S = {-1,1,2}