[tex]\displaystyle\bf\\\left \{ {{\dfrac{x}{6} \geq \dfrac{x+1}{7} } \atop {3(x+2)+7 > 4(x-3)+15}} \right. \\\\\\\left \{ {{\dfrac{x}{6}\cdot 42 \geq \dfrac{x+1}{7}\cdot42 } \atop {3x+6+7 > 4x-12+15}} \right. \\\\\\\left \{ {{7x\geq 6x+6} \atop {3x+13 > 4x+3}} \right. \\\\\\\left \{ {{7x-6x\geq 6} \atop {3x-4x > 3-13}} \right. \\\\\\\left \{ {{x\geq 6} \atop {-x > -10}} \right. \\\\\\\left \{ {{x\geq 6} \atop {x < 10}} \right. \\\\\\x\in\Big[6 \ ; \ 10\Big)\\\\\\Otvet \ : \ 6[/tex]