Question

Determinati elementele comune multimilor A = ( x e Z | 4-3(5-3x) mai mic sau egal 16 ) si B= (x e Z | 11(2x+1) - 3(x+9 ) mai mare decat 6(3x-2) . Ajutati-ma, va rog !

Answer 1

Elementele comune, adica multimea A intersectie cu multimea B
A int B = ?


A={x | xeZ, 4-3(5-3x)≤16}

4-3(5-3x)≤16
4-15+9x≤16
9x≤16+11
9x≤27
x≤3 eZ
x e (-∞;3] cu conditia xeZ

B={x | xeZ, 11(2x+1)-3(x+9)>6(3x-2) }

11(2x+1)-3(x+9)>6(3x-2)
22x+11-3x-27>18x-12
19x-16>18x-12
19x-18x>-12+16
x>4 eZ
x e (4;+∞) cu conditia xeZ


A int B = (-∞;3] int (4;+∞) = ∅

Raspuns: Multimile nu au nici un element comun

*int inseamna intersectie..