Question

СРОЧНО!!!!! 35 БАЛЛОВ!!! ПОДРОБНО ПОЖАЛУЙСТА!

Answer 1

$1)\ \ |x+1|+|x-2|=3\\\\znaki\ (x+1):\ \ ---(-1)+++++++++\\znaki\ (x-2):\ \ --------(2)+++++\\\\a)\ \ x\leq -1:\ |x+1|=-x-1\ ,\ |x-2|=-x+2\ ,\\\\|x+1|+|x-2|=-x-1-x+2=-2x+1\ ,\ \ -2x+1=3\ ,\\\\2x=-2\ \ ,\ \ \underline {\ x=-1\in (-\infty ;-1\ ]\ }\\\\b)\ \ -1<x\leq 2:\ \ |x+1|=x+1\ ,\ \ |x-2|=-x+2\ ,\\\\|x+1|+|x-2|=x+1-x+2=3\ \ ,\ \ 3=3\ \ ,\ \ \underline {x\in (-1;2\ ]\ }$

$c)\ \ x>2\ \ |x+1|=x+1\ \ ,\ \ |x-2|=x-2\ ,\\\\|x+1|+|x-2|=x+1+x-2=2x-1\ \ ,\ \ 2x-1=3\ \ ,\\\\2x=4\ \ ,\ \ \underline {x=2\notin (\, 2;+\infty )\ }\\\\Otvet:\ \ x\in [-1\, ;\, 2\ ]\ .$

$2)\ \ |5x-2|\leq 4\ \ \ \Rightarrow \ \ \ \ -4\leq 5x-2\leq 4\ \ ,\\\\-2\leq 5x\leq 6\ \ ,\ \ \ -\dfrac{2}{5}\leq x\leq \dfrac{6}{5}\ \ ,\ \ \ \ -0,4\leq x\leq 1,2\\\\Otvet:\ \ x\in [-0,4\ ;\, 1,2\ ]$