Решите неравенство: 1)|x-3| больше =1,8 2)|2-x| больше 1\3 3)|3-x| меньше 1,2 4) |4+х| меньше =1,8 5)|0,5-х| больше = 3 6) |6-x| меньше = 2,1 Заранее спасибо!

1) [latex]|x-3| \geq 1.8[/latex] [latex]x-3 \geq 1.8[/latex]       или       [latex]x-3 \leq -1.8[/latex] [latex]x \geq 1.8+3[/latex]       или       [latex]x \leq -1.8+3[/latex] [latex]x \geq 4.8[/latex]            или       [latex]x \leq 1.2[/latex] ----------[1.2]-----------[4.8]--------------- ///////////                       ////////////////// [latex]x[/latex] ∈ [latex](-[/latex] ∞ [latex];1.2][/latex] ∪ [latex][4.8;+[/latex] ∞ [latex])[/latex] 2) [latex]|2-x|\ \textgreater \ \frac{1}{3} [/latex] [latex]2-x\ \textgreater \ \frac{1}{3} [/latex]         или       [latex]2-x\ \textless \ - \frac{1}{3} [/latex] [latex]-x\ \textgreater \ \frac{1}{3}-2 [/latex]       или       [latex]-x\ \textless \ - \frac{1}{3} -2[/latex] [latex]x\ \textless \ 1 \frac{2}{3} [/latex]              или       [latex]x\ \textgreater \ 2 \frac{1}{3} [/latex] ----------(1 2/3)-----------(2 1/3)--------------- ///////////                         ////////////////// [latex]x[/latex] ∈ [latex](-[/latex] ∞ [latex];1\frac{2}{3})[/latex] ∪ [latex](2\frac{2}{3};+[/latex] ∞ [latex])[/latex] 3) [latex] | 3-x|\ \textless \ 1.2[/latex] [latex] \left \{ {{3-x\ \textless \ 1.2} \atop {3-x\ \textgreater \ -1.2}} \right. [/latex] [latex] \left \{ {{-x\ \textless \ 1.2-3} \atop {-x\ \textgreater \ -1.2-3}} \right. [/latex] [latex] \left \{ {{-x\ \textless \ -1.8} \atop {-x\ \textgreater \ -4.2}} \right. [/latex] [latex] \left \{ {{x\ \textgreater \ 1.8} \atop {x\ \textless \ 4.2}} \right. [/latex] ---------(1.8)-----------(4.2)----------              ///////////////// [latex]x[/latex] ∈ [latex](1.8;4.2)[/latex] 4) [latex] |4+x | \leq 1.8[/latex] [latex] \left \{ {{4+x \leq 1.8} \atop { 4+x \geq -1.8}} \right. [/latex] [latex] \left \{ {{x \leq 1.8-4} \atop { x \geq -1.8-4}} \right. [/latex] [latex] \left \{ {{x \leq -2.2} \atop { x \geq -5.8}} \right. [/latex] ----------[-5.8]---------[-2.2]-----------                //////////////// [latex]x[/latex] ∈ [latex][-5.8;-2.2][/latex] 5) [latex]|0.5-x| \geq 3[/latex] [latex]0.5-x\geq 3[/latex]        или       [latex]0.5-x \leq - 3[/latex] [latex]-x\geq 3-0.5[/latex]    или       [latex]-x \leq -3-0.5[/latex] [latex]-x\geq 2.5[/latex]          или       [latex]-x \leq -3.5[/latex] [latex]x \leq -2.5[/latex]          или        [latex]x \geq 3.5[/latex] ----------[-2.5]-----------[3.5]--------------- ///////////                        ////////////////// [latex]x[/latex] ∈ [latex](-[/latex] ∞ [latex];-2.5][/latex] ∪ [latex][3.5;+[/latex] ∞ [latex])[/latex] 6) [latex] |6-x | \leq 2.1 [/latex] [latex] \left \{ {{ 6-x \leq 2.1} \atop { 6-x \geq -2.1}} \right. [/latex] [latex]\left \{ {{ -x \leq 2.1-6} \atop { -x \geq -2.1-6}} \right. [/latex] [latex]\left \{ {{ -x \leq -3.9} \atop { -x \geq -8.1}} \right. [/latex] [latex]\left \{ {{ x \geq 3.9} \atop { x \leq 8.1}} \right. [/latex] ----------[3.9]---------[8.1]-----------                //////////////// [latex]x[/latex] ∈ [latex][3.9;8.1][/latex]

Ответ ответ ответ ответ ответ