Решить неравенство I3 ͯ +1I больше 2*3 ͯ -2

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

[latex]|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) \\ [/latex]