[tex]\displaystyle\bf\\\Big|\frac{3}{x-7} \Big| > \frac{6}{7} \\\\ODZ \ : \ x\neq 7\\\\1)\\\\\frac{3}{x-7} < -\frac{6}{7} \\\\\\\frac{3}{x-7} +\frac{6}{7} < 0\\\\\\\frac{21+6x-42}{x-7} < 0\\\\\\\frac{6x-21}{x-7} < 0\\\\\\\frac{x-3,5}{x-7} < 0\\\\\\+ + + + + (3,5)- - - - - (7)+ + + + + \\\\x\in(3,5 \ ; \ 7)\\\\2)\\\\\frac{3}{x-7} > \frac{6}{7} \\\\\\\frac{3}{x-7} -\frac{6}{7} > 0\\\\\\\frac{21-6x+42}{x-7} > 0\\\\\\\frac{-6x+63}{x-7} > 0\\\\\\\frac{x-10,5}{x-7} < 0[/tex]
[tex]\displaystyle\bf\\+ + + + + (7)- - - - - (10,5)+ + + + + \\\\x\in(7 \ ; \ 10,5)\\\\\\Otvet \ : \ x\in(3,5 \ ; \ 7)\cup(7 \ ; \ 10,5)[/tex]
Целые решения неравенства : 4 ; 5 ; 6 ; 8 ; 9 ; 10
Их сумма равна : 4 + 5 + 6 + 8 + 9 + 10 = 42
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[tex]\displaystyle\bf\\\Big|\frac{3}{x-7} \Big| > \frac{6}{7} \\\\ODZ \ : \ x\neq 7\\\\1)\\\\\frac{3}{x-7} < -\frac{6}{7} \\\\\\\frac{3}{x-7} +\frac{6}{7} < 0\\\\\\\frac{21+6x-42}{x-7} < 0\\\\\\\frac{6x-21}{x-7} < 0\\\\\\\frac{x-3,5}{x-7} < 0\\\\\\+ + + + + (3,5)- - - - - (7)+ + + + + \\\\x\in(3,5 \ ; \ 7)\\\\2)\\\\\frac{3}{x-7} > \frac{6}{7} \\\\\\\frac{3}{x-7} -\frac{6}{7} > 0\\\\\\\frac{21-6x+42}{x-7} > 0\\\\\\\frac{-6x+63}{x-7} > 0\\\\\\\frac{x-10,5}{x-7} < 0[/tex]
[tex]\displaystyle\bf\\+ + + + + (7)- - - - - (10,5)+ + + + + \\\\x\in(7 \ ; \ 10,5)\\\\\\Otvet \ : \ x\in(3,5 \ ; \ 7)\cup(7 \ ; \ 10,5)[/tex]
Целые решения неравенства : 4 ; 5 ; 6 ; 8 ; 9 ; 10
Их сумма равна : 4 + 5 + 6 + 8 + 9 + 10 = 42