Question

Решите неравенства с объяснением​

Answer 1

$1)~\big|x-3\big|\geq 1,8~~~~\Leftrightarrow~~~~\left[\begin{array}{c}x-3\geq1,8~~~~~~~~~~\\-\Big(x-3\Big)\geq 1,8~~~~\big|\cdot(-1)\end{array}\right.\\\\\\\left[\begin{array}{c}x\geq3+1,8 \\x-3\leq -1,8\end{array}\right.~~~\Leftrightarrow~~~\left[\begin{array}{c}x\geq4,8 \\x\leq 1,2\end{array}\right.\\\\\\\boxed{\boldsymbol{x\in(-\infty;1,2]\cup[4,8;+\infty)}}$

$1)~\big|3-x\big|< 1,2~~~~\Leftrightarrow\\\\-1,2<3-x<1,2~~~~\Big|-3\\\\-4,2<-x<-1,8~~~~\Big|\cdot(-1)\\\\~~~~4,2>x>1,8~~~~~~~~\boxed{\boldsymbol{x\in(1,8;4,2)}}$

Answer 2

Ответ:

Пошаговое объяснение:

1) |x-3|≥1,8

При x-3≥0: x-3≥18; x≥1,8+3; x≥4,8

При x-3<0: 3-x≥1,8; x≤3-1,8; x≤1,2

x∈(-∞; 1,2]∪[4,8; +∞)

2) |3-x|<1,2

При 3-x≥0: 3-x<1,2; x>3-1,2; x>1,8

При 3-x<0: x-3<1,2; x<1,2+3; x<4,2

x∈(1,8; 4,2)