Question

rezolvati in multimea nr. intregi inecuatia |x-2|(7-|2x-1|)>0

Answer 1

ptr. x -2 ≥ 0  x ≥ 2   |x - 2| = x-2  |2x - 1| = 2x -1
(x - 2) (8-2x) > 0
a)   x -2 > 0  x > 2     8-2x > 0  2x< 8   x < 4
x > 2 ∪ x < 4 ⇒ x = 3 
b)  2x - 1 < 0      x < 1/2  |2x - 1| = 1-2x    |x -2| = 2-x
(2-x)(6+2x) > 0
2-x > 0      x < 2       6 + 2x > 0    x > -3
x > -3 ∪ x <2 ⇒ x ∈ {-2,-1,0,1}