Question

1. Rezolvaţi inecuaţiile:
a)4x−5<3x− 2, xe N;
c) 2x-1| + 3x ≤ 3(x+2), x = N*;
b) 7x+9>3x-7, xe Z;
d) 3x +21-2x ≤2(2-x)+5, xe Z.
Va rog mult urgentt!!❤️❤️

Answer 1

Explicație pas cu pas:

a)

$4x−5<3x− 2 \\ 4x - 3x < - 2 + 5 \\\implies x < 3$

x ∈ N => x ∈ {0; 1; 2}

b)

$7x+9>3x-7 \\ 7x - 3x > - 7 - 9 \\ 4x > - 16 \\ \implies x > - 4$

x ∈ Z => x ∈ {-3; -2; -1; 0; 1; ...}

c)

$2x - 1 + 3x \leqslant 3(x + 2) \\ 5x - 1\leqslant 3x + 6 \\ 5x - 3x \leqslant 6 + 1 \\ 2x \leqslant 7 \\ x \leqslant \frac{7}{2} \iff x \leqslant 2 \frac{1}{2}$

x ∈ N* => x ∈ {1; 2}

d)

$3x +21-2x \leqslant 2(2-x)+5 \\ x + 21 \leqslant 4 - 2x + 5 \\ x + 2x \leqslant 9 - 21 \\ 3x \leqslant 12 \implies x \leqslant 4$

x ∈ Z => x ∈ {...; -1; 0; 1; 2; 3; 4}