Question

3. Rezolvați în mulțimea numerelor naturale inecuațiile: a) 3(x-1) ≤2(x-3)+7; c) 3(4-3x) + 2(5x - 3) ≤ 12-x; b) 2x+9-3(x-2) ≤4(3-x)+18; d) 3(2x-5)-4(1-2x) ≤ 6(2x + 3)-25.​

Answer 1

Răspuns:

Explicație pas cu pas:

a) 3(x-1) ≤ 2(x-3)+7 <=>

3x-3 ≤ 2x-6+7 <=>

3x-2x ≤ 1+3 => x ≤ 4 =>

x ∈ {0 ; 1 ; 2 ; 3 ; 4}

b) 2x+9-3(x-2) ≤ 4(3-x)+18 <=>

2x+9-3x+6 ≤ 12-4x+18 <=>

-x+15 ≤ 30-4x =>

4x-x ≤ 30-15 =>

3x ≤ 15  I:3 => x ≤ 5 =>

x ∈ {0 ; 1 ; 2 ; 3 ; 4 ; 5}

c) 3(4-3x) + 2(5x - 3) ≤ 12-x <=>

12-9x+10x-6 ≤ 12-x <=>

x+6 ≤ 12-x <=>

x+x ≤ 12-6 =>

2x ≤ 6  I:2 => x ≤ 3 =>

x ∈ {0 ; 1 ; 2 ; 3}

d) 3(2x-5)-4(1-2x) ≤ 6(2x + 3)-25 <=>

6x-15-4+8x ≤ 12x+18-25 <=>

14x-19 ≤ 12x -7 =>

14x-12x ≤ 19-7 =>

2x ≤ 12  I:2 => x ≤ 6 =>

x ∈ x ∈ {0 ; 1 ; 2 ; 3 ; 4 ; 5 ; 6}