Question

|||2x-3|+2|-5|=6 и |||2x+7|-3|+6+=6

Answer 1

$1)\quad |\; |\, |2x-3|+2|-5|=6\\\\|x|=a\; \; \Rightarrow \; \; x=\pm a\; ;\; \; \; \; |x| \geq 0\\\\a)\quad |\, |2x-3|+2|-5=\pm 6\; \; \Rightarrow \left [ {{|\, |2x-3|+2|-5=6} \atop {|\, |2x-3|+2|-5=-6}} \right. \\\\ \left \{ {{|\, |2x-3|+2|=11} \atop {|\, |2x-3|+2|=-1\ \textless \ 0}} \right. \; \; \Rightarrow |\, |2x-3|+2|=11\\\\b)\quad |2x-3|+2=\pm 11\; \; \Rightarrow \; \; \left [ {{|2x-3|=9} \atop {|2x-3|=-13\ \textless \ 0}} \right. \; \; \Rightarrow \; \; |2x-3|=9\\\\c)\quad 2x-3=\pm 9\; \; \Rightarrow$

$\left [ {{2x=12} \atop {2x=-6}} \right. \; \; \left [ {{x=6} \atop {x=-3}} \right. \\\\Otvet:\; \; x=6,\; x=-3\; .$

$2)\quad |\, |\, |2x+7|-3|+6|=6\\\\a)\; \; \left [ {{||2x+7|-3|+6=6} \atop {||2x+7|-3|+6=-6}} \right. \; \left [ {{||2x+7|-3|=0} \atop {||2x+7|-3|=-12\ \textless \ 0,\; net\; reshenij }} \right. \\\\b)\; \; ||2x+7|-3|=0\; \; \Rightarrow \; \; |2x+7|-3=0 \\\\c)\quad |2x+7|=3\; \; \Rightarrow \; \; \left [ {{2x+7=3} \atop {2x+7=-3}} \right. \; \left \{ {{2x=-4} \atop {2x=-10}} \right. \; \left [ {{x=-2} \atop {x=-5}} \right. \\\\Otvet:\; x=-2,\; x=-5\; .$

Answer 2

||2x-3|+2|-5=6 или ||2x-3|+2|-5=-6

|2x-3|+2=11            |2x-3|+2=-1
2x-3=9или
 2x-3=-9                  | 2x-3|=-3 решений нет
Ответ:6; -3