Question

1017. Решите неравенства:
1) |9 – х| = 2;
5) |x – 5| <11;
6) |6 – x| > 7.
ДАЮ 20 БАЛЛОВ​

Answer 1

$displaytyle tt 1) : |9-x|=2\\ displaytyle tt 9-x=2\displaytyle tt 9-x=-2\\displaytyle tt -x=-7\displaytyle tt -x=-11\\ displaytyle tt boxed{bold{x_1=7}}\displaytyle tt boxed{bold{x_2=11}}$

$displaytyle tt 5): |x-5|<11\\displaytyle tt x-5<11, : : x-5geq 0\displaytyle tt -(x-5)<11, : : x-5<0\\displaytyle tt x<16, : : xgeq 5\displaytyle tt x>-6, : : x<5\\displaytyle tt xin [5;:16)\displaytyle tt xin (-6;:5)\\displaytyle tt boxed{bold{xin(-6;:16)}}$

$displaytyle tt 6) : |6-x|>7\\ displaytyle tt 6-x>7, : : 6-xgeq 0\displaytyle tt -(6-x)>7, : : 6-x<0\\ displaytyle tt x<-1, : : xleq 6\displaytyle tt x>13, : : x>6\\ displaytyle tt xin(-infty; : -1)\displaytyle tt xin(13; : +infty)\\ displaytyle tt boxed{bold{xin(-infty; : -1)cup (13; : +infty)}}$