@gianna_giovanna
Ciao e buona sera.
{(2·x - 3)/(6 - 10·x) ≤ 0
{1/4·x^2 > (1/2·x - 1/3)^2
-----------------------------
Risolviamo la 1^ disequazione:
N(x)
--------------------------------[3/2]++++++++++++>x
D(x)
++++++++++(3/5)------------------------------------>x
Rapporto:
------------------(3/5)+++++[3/2]--------------------->x
Soluzione: x < 3/5 ∨ x ≥ 3/2
Risolviamo la 2^ disequazione:
1/4·x^2 > (1/2·x - 1/3)^2
1/4·x^2 > x^2/4 - x/3 + 1/9-------> 1/9 - x/3 < 0
quindi: x > 1/3
{*************(3/5)...............[3/2]*****
{............(1/3)***************************
Soluzione sistema:
1/3 < x < 3/5 ∨ x ≥ 3/2