Question

Aflați mulțimea E={x€Z| |2x+3|1/4}​

Answer 1

Răspuns:

E=∅

Explicație pas cu pas:

-1/4<2x+3<1/4  | inmultim cu 4

-1<8x+12<1  | scadem 12

-13<8x<-11  | i partim la 8

-13/8<x<-11/8  |transformam in fractie zecimala

E=(-1,625;-1,375)∩Z=∅

extra

sa ne amintim!

|x|<a, unde a>0⇔ -a<x<a

si |x|=a, pt a>0 x=a sau exclusiv x=-a

|x|>a unde a>0⇔ x∈(-∞;-a)∪(a;∞)

Answer 2

$\it |2x+3|<\dfrac{1}{4} \Rightarrow -\dfrac{1}{4}<2x+3<\dfrac{1}{4}|_{-3} \Rightarrow-\dfrac{13}{4}<2x<-\dfrac{11}{4}\Big|_{\cdot\dfrac{1}{2}}\Rightarrow\\ \\ \\ \Rightarrow-\dfrac{13}{8}<x<-\dfrac{11}{8} \Rightarrow-1\dfrac{5}{8}< x <-1\dfrac{3}{8} \ \ \ \ (1)\\ \\ \\ x\in\mathbb{Z}\ \ \ \ \ (2)\\ \\ (1),\ (2) \Rightarrow E = \varnothing$