Question

Buna ziua.
Am nev de ajutor la un ex in care spune asa:
Sa se rezolve:
a)[x]=3
b)[x+2]=-3
c)[2x]=3
d)[3x+1 TOTUL supra 2]=5

Answer 1

Definitie pt. parte intreaga
[x]=a ⇔ a ≤ x < a+1

a) [x]=3 ⇔ 3 ≤ x < 4 ⇔ x ∈ [3,4)
b) [x+2]=-3 ⇔ -3 ≤ x+2 <-2  |-2 ⇔-5 ≤ x < -4 ⇔ x∈[-5,-4)
c) [2x]=3 ⇔ 3 ≤ 2x < 4  |:2 ⇔ 3/2 ≤ x < 2 ⇔ x∈[3/2,2)
d)$[ \frac{3x+1}{2} ]=5$⇔$5 \leq \frac{3x+1}{2} \ \textless \ 6$ ⇔
$10 \leq 3x+1\ \textless \ 12$ ⇔ $9 \leq 3x\ \textless \ 11$ ⇔ 
$3 \leq x\ \textless \ \frac{11}{3}$ ⇔ x∈[3,11/3)