Question

Fie mulțimile A și B

Answer 1

Răspuns:

a)

-3≤4x-1≤5   |+1

$\frac{-2}{4}$≤x≤$\frac{6}{4}$

$\frac{-1}{2}$≤x≤$\frac{3}{2}$

Deci:

A=[$\frac{-1}{2},\frac{3}{2}$]

|5x+2|<3

-3<5x+2<3   |-2

-5<5x<1   |:5

-1<x<$\frac{1}{5}$

Deci:

B=($-1,\frac{1}{5}$)

b)

AUB=($-1,\frac{3}{2}$]

A∩B=[$-\frac{1}{2} ,\frac{1}{5}$)

A\B=[$\frac{1}{5} ,\frac{3}{2}$]

B\A=($-1,\frac{-1}{2}$)