Question

Решить неравенство i3 ͯ +1i > 2*3 ͯ -2

Answer 1

При любом х ∈(-∞;+∞)
$3 ^{x}\ \textgreater \ 0$
$3 ^{x}+1\ \textgreater \ 0$ и подавно, поэтому
$|3 ^{x}+1|=3 ^{x}+1$
Решаем неравенство
$3 ^{x}+1 \textgreater \ 2\cdot3 ^{x} -2 \\ \\ 3 ^{x}-2\cdot3 ^{x}\ \textgreater \ -1 -2 \\ \\- 3 ^{x}\ \textgreater \ -3$

$3 ^{x}\ \textless \ 3 \\ \\ x\ \textless \ 1$
x∈(-∞;1)

Answer 2

$|3^x+1|\ \textgreater \ 2*3^x-2 \\ 3^x\ \textgreater \ 0 \iff 3^x+1\ \textgreater \ 0 \\ |3^x+1|\ \textgreater \ 2*3^x-2 \iff 3^x+1\ \textgreater \ 2*3^x-2 \iff -3^x\ \textgreater \ -3 \\ \iff 3^x\ \textless \ 3^1 \iff x\ \textless \ 1 \\ x\in (-\infty;1) \\$