Question

4.Se consideră mulțimea A={x€ℤ||2x+1|<7}.Suma elementelor mulțimii A este egală cu:
a)-4;
b)-3;
c)-2;
d)-1;​

Answer 1

$|2x+1| < 7\iff-7 < 2x+1 < 7\\-8 < 2x < 6\\-4 < x < 3 \implies x \in(-4,3) \\(-4,3) \cap \mathbb{Z}=\{-3,-2,-1,0,1,2\}=A\\(-3)+(-2)+(-1)+0+1+2=-3-2-1+0+1+2=\boxed{-3}$