Question

|5х-1|<6
Решите неравенство
С чертежом пожалуйста

Answer 1

$|5x-1|<6\\\\a)\ \ 5x-1\geq 0\ \ ,\ \ x\geq \dfrac{1}{5}\ \ \to \ \ \ |5x-1|=5x-1\ \ ,\ \ \ 5x-1<6\ \ ,\ \ 5x<7\ ,\\\\x<\dfrac{7}{5}\ \ \ \to \ \ \ \dfrac{1}{5}\leq x<\dfrac{7}{5}\ \ ,\ \ \ \ 0,2\leq x<1,4\\\\b)\ \ 5x-1<0\ \ ,\ \ x<\dfrac{1}{5}\ \ \to \ \ \ |5x-1|=-5x+1\ \ ,\ \ \ -5x+1<6\ \ ,\\\\\\-5x<5\ \ ,\ \ x>-1\ \ \ \to \ \ \ -1<x<0,2\\\\Otvet:\ \ x\in(-1\, ;\, 0,2\, )\cup [\ 0,2\ ;\ 1,4\, )=\underline {\ (-1\ ;\ 1,4\, )\ }\ .$