log0.2(3x-5)>=log0.2(x+2)

[tex]log_{0.2}(3x-5) \geq log_{0.2}(x+2)[/tex]
ОДЗ:
[tex] \left \{ {3x-5\ \textgreater \ 0} \atop {x+2\ \textgreater \ 0}} \right. [/tex]
[tex] \left \{ {3x\ \textgreater \ 5} \atop {x\ \textgreater \ -2}} \right. [/tex]
[tex] \left \{ {x\ \textgreater \ 1 \frac{2}{3} } \atop {x\ \textgreater \ -2}} \right. [/tex]
[tex]x[/tex] ∈ [tex](1 \frac{2}{3} ;+[/tex] ∞ [tex])[/tex]

[tex]3x-5 \leq x+2[/tex]
[tex]3x-x \leq 2+5[/tex]
[tex]2x \leq 7[/tex]
[tex]x \leq 3.5[/tex]

------------------------------[3.5]-------------------
/////////////////////////////////
-------(1 2/3)----------------------------------------
                ///////////////////////////////////////
Ответ: [tex](1 \frac{2}{3};3.5] [/tex]