Question

Determinați x astfel încât: 3,(2)+x<9,(7) în N

Answer 1

3,(2) = $\frac{32-3}{9} = \frac{29}{9}$
9,(7) = $\frac{97-9}{9} = \frac{88}{9}$
$\frac{29}{9} + x \ \textless \ \frac{88}{9}$

Amplificam la x cu 9 :

$29+9x\ \textless \ 88$  | - 29
$9x \ \textless \ 88-29$
$9x\ \textless \ 59$
$x\ \textless \ \frac{59}{9}$
x < 6,(5)
x ∈ {0,1,2,3,4,5,6}

Answer 2

3,[2]+x<9,[7]
⇒32-3/9+x<97-9/9
⇒29/9+x<88/9
⇒x<88/9-29/9
⇒x<59/9⇒x<6,[5]⇒x∈N;
⇒x∈[0,1,2,3,4,5,6];