Question

Numerele naturale solutii ale inecuatiei |x|• (|x-3|-2) <0 sunt:
A{1,2,3,4,5}
B{2,3,4}
C{1,2,3,4}
D{2,3,4,5}

Answer 1

Răspuns:

B

Explicație pas cu pas:

$|x| \cdot ( |x - 3| - 2) < 0$

$|x| \geqslant 0 \implies |x - 3| - 2 < 0$

$|x - 3| < 2 \\ - 2 < x - 3 < 2 \\ - 2 + 3 < x < 2 + 3 \\ 1 < x < 5 \\ x \in \mathbb{N} \implies S = \Big\{ 2; 3; 4 \Big\}$