Question

3. Rezolvati n multimea numerelor naturale inecuatiile:
a) 3(x - 1) ≤ 2(x - 3) + 7;
b) 2x +9 - 3(x-2) ≤4(3 -x) + 18;
c) 3(4 - 3x) + 2(5x - 3) ≤ 12 - x;
d) 3(2x - 5) - 4(1 - 2x) ≤6(2x + 3) - 25.
DAU COROANA

Answer 1

$\it a)\ \ 3(x-1)\leq2(x-3)+7 \Rightarrow 3x-3\leq2x-6+7 \Rightarrow\\ \\ \Rightarrow 3x-2x\leq-6+7+3 \Rightarrow x\leq4 \Rightarrow x\in\{0,\ \ 1,\ \ 2,\ \ 3,\ \ 4\}\\ \\ \\ d)\ \ 3(2x-5)-4(1-2x)\leq6(2x+3)-25 \Rightarrow 6x-15-4+8x\leq12x+18-25 \Rightarrow \\ \\ \Rightarrow 6x+8x-12x\leq18-25+4+15 \Rightarrow 2x\leq12\Big|_{:2} \Rightarrow x\leq6 \Rightarrow \\ \\ \Rightarrow x\in\{0,\ \ 1,\ \ 2,\ \ 3,\ \ 4,\ \ 5,\ \ 6\}$

Answer 2

Răspuns:

a) 3(x - 1) ≤ 2(x - 3) + 7

3x-3 ≤2x-6+7

3x-2x ≤ -6+7+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

2x-3x+4x ≤12+18-15

3x ≤ 15

x ≤ 15:3

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+x ≤ 12-12+6

2x ≤ 6

x ≤ 6:2

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-12x ≤ 18-25+15+4

2x ≤ 12

x ≤ 12:2

x ≤ 6

x ∈ {0,1,2,3,4,5,6}