Question

Rezolvati in R inecuatia
$\frac{3x-7}{6} \geq \frac{5-6x}{4}$

[tex] \frac{x-1}{4} + \frac{x+3x}{2} mai mic 1- \frac{x}{6}
[/tex]
(x-3)(x-6) mai mic (x-1)(x-2)
Varog ajutor dau 20 puncte su coronita
Pina la ora 08:00

Answer 1

lasa coronita. vezi daca te ajuta 
deci pt asa (3x-7)/6≥(5-6x)/4
4×(3x-7)≥6×(5-6x)
12x-28≥30-36x
12x+36x≥28+30
48x≥58
x≥58/48 care se simplifica cu 2⇒x≥29/24⇒x∈[29/24,+∞)
pt (x-1)/4+(x+3x)/2 <1-x/6
(x-1)/4+(x+3x)/2 aduc la acelasi numitor=(x-1)/4+2×(x+3x)/4=(x-1+2x+6x)/4=(9x-1)/4
1-x/6 aduc la acelasi numitor= 1×6/6-x/6=(6-x)/6
acum avem (9x-1)/4<(6-x)/6
6×(9x-1)<4×(6-x)
54x-6<24-4x
54x+4x<24+6
58x<30⇒x<30/58 care se simplifica cu 2⇒x<29/15⇒x∈(-∞,29/15)
deci ai (x-3)(x-6)<(x-1)(x-2)
x²-6x-3x+18<x²-2x-x+2
x²-9x+18<x²-3x+2
x²-9x-x²+3x<2-18
-9x+3x<-16
-6x<-16
x<-16/-6
x<16/6 care se simplifica cu 2 si x<8/3⇒x∈(-∞,8/3)