Question

1) rezolvati inecuatiile:
a) 0,1x+3,2<3,5, x∈ N
b) 3,7X+2,5 >2,5x +1,06, x∈Z
c) 0,5-x\3<1\6 +0,5x,x∈Z
REZOLVARE COMPLETA!

Answer 1

a) 0,1x + 3,2 < 3,5 => 0,1x < 0,3 => x < 3 => S = {0, 1, 2}
b) 3,7x + 2,5 > 2,5x + 1,06 => 1,2x + 2,5 > 1,06 => 1,2x > -1,44 => x > -1,2 => S = {-1, 0, 1, 2, 3, 4, ...}
c) 0,5 - x/3 < 1/6 + 0,5 => 3/6 - 2x/6 < 1/6 + 3/6 (am adus la acelasi numitor si acum inmultim cu 6 relatia, ca sa scapam de el) => 3 - 2x < 1 + 3 => 3 - 2x < 4 => -2x < 1 => x > -1/2 => S = {0, 1, 2, 3, 4, ...}