[tex]\displaystyle\bf\\ODZ:\\\\\left \{ {{x\neq 0} \atop {10+3x > 0}} \right. \ \ \Rightarrow \ \ \left \{ {{x\neq 0} \atop {x > -3\dfrac{1}{3} }} \right. \ \ \Rightarrow \ \ x\in\Big(-3\frac{1}{3} \ ; \ 0\Big)\cup\Big(0 \ ; \ +\infty\Big)\\\\\\\log_{0,3} x^{2} \geq \log_{0,3} (10+3x)\\\\\\0 < 0,3 < 1 \ \ \ \Rightarrow \ \ \ x^{2} \leq 10+3x\\\\x^{2} -3x-10\leq 0\\\\(x+2)\cdot(x-5)\leq 0\\\\\\+ + + + + [-2] - - - - - [5] + + + + + \\\\x\in\Big[-2 \ ; \ 5\Big][/tex]
С учётом ОДЗ окончательный ответ :
[tex]\displaystyle\bf\\x\in\Big[-2 \ ; \ 0\Big) \ \cup \ \Big(0 \ ; \ 5\Big][/tex]
Целых решений 7 : - 2 ; - 1 ; 1 ; 2 ; 3 ; 4 ; 5
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[tex]\displaystyle\bf\\ODZ:\\\\\left \{ {{x\neq 0} \atop {10+3x > 0}} \right. \ \ \Rightarrow \ \ \left \{ {{x\neq 0} \atop {x > -3\dfrac{1}{3} }} \right. \ \ \Rightarrow \ \ x\in\Big(-3\frac{1}{3} \ ; \ 0\Big)\cup\Big(0 \ ; \ +\infty\Big)\\\\\\\log_{0,3} x^{2} \geq \log_{0,3} (10+3x)\\\\\\0 < 0,3 < 1 \ \ \ \Rightarrow \ \ \ x^{2} \leq 10+3x\\\\x^{2} -3x-10\leq 0\\\\(x+2)\cdot(x-5)\leq 0\\\\\\+ + + + + [-2] - - - - - [5] + + + + + \\\\x\in\Big[-2 \ ; \ 5\Big][/tex]
С учётом ОДЗ окончательный ответ :
[tex]\displaystyle\bf\\x\in\Big[-2 \ ; \ 0\Big) \ \cup \ \Big(0 \ ; \ 5\Big][/tex]
Целых решений 7 : - 2 ; - 1 ; 1 ; 2 ; 3 ; 4 ; 5