Question

Rezolvați în N inecuația:

12-4(x+3/8)≥x+11/2

Answer 1

12-4x-12/8>= x+11/2
12-4x-3/2>= x+11/2
-5x>= 11/2 +3/2 -12
-5x>=7-12
-5x>= -5. |:(-5)
x<=1
===> x apartine (infinit; 1]
Se schimba semnele <, > si celelalte cand inmultesti cu un numar negativ
Am notat >= mai mare sau egal
Succese

Answer 2

$\it x\in\mathbb{N}\\ \\ 12-4\Big(x+\dfrac{3}{8}\Big)\geq x+\dfrac{11}{2} \Rightarrow 12-4x+\dfrac{3}{2}\geq x+\dfrac{11}{2}|_{-\frac{3}{2}} \Rightarrow\\ \\ \\ \Rightarrow 12-4x\geq x+4 \Rightarrow12-4\geq x+4x \Rightarrow 5x\leq8 \Rightarrow x\in\{0,\ \ 1\}$