Question

numarul elementelor multimii a={x€n*/ 2x-1) mai mic decat 10-x}
x-(x-1)/3=3 are solutia

Answer 1

Primul exercitiu:
2x-1<10-x
3x<11
x<11/3
Dar x∈N
Deci x∈{0,1,2,3}
A={0,1,2,3}
cardA=4

Al doilea:

x-(x-1)/3=3
Inmultim totul cu 3
3x-(x-1)=9
4x+1=9
4x=8
x=2

Answer 2

1. 2x-1<10-x
⇒2x<11-x
⇒x<[11-x]/2⇒x∈N;
⇒[11-x]/2=[11-1]/2=10/2=5;
⇒[11-x]/2=[11-3]/2=8/2=4;
⇒[11-x]/2=[11-5]/2=6/2=3⇒5<3⇒fals;
⇒x=[1,3]⇒1<5; 3<4;
⇒numarul elementelor multimii este card a=2;

2. 3x/3-[x-1]/3=3
⇒3x-x-1=9
⇒2x=10⇒x=5⇒solutia este x=5;