Решите неравенство: 1) 3-2(и-1) больше 8+и; 2) 5(и+2)+14 меньше 6-и; 3) 1/4(3+8и)больше или равно 6,25+и; 4)4(и+3) меньше 3(и+2); 5) 3(2и+1) больше 5(и-1); 6) 3/5(5и-2/3) меньше и+7,6;
Решите неравенство:
1) 3-2(и-1)>8+и;
2) 5(и+2)+14<6-и;
3) 1/4(3+8и)больше или равно 6,25+и;
4)4(и+3)<3(и+2);
5) 3(2и+1)>5(и-1);
6) 3/5(5и-2/3)<и+7,6;
Ответ(ы) на вопрос:
Гость
1)
[latex]3-2(u-1)\ \textgreater \ 8+u[/latex]
[latex]3-2u+2\ \textgreater \ 8+u[/latex]
[latex]5-2u\ \textgreater \ 8+u[/latex]
[latex]-2u-u\ \textgreater \ 8-5[/latex]
[latex]-3u\ \textgreater \ 3[/latex]
[latex]u\ \textless \ -1[/latex]
-------------(-1)-----------------
//////////////
[latex]u[/latex] ∈ [latex](-[/latex] ∞ [latex];-1)[/latex]
2)
[latex]5(u+2)+14\ \textless \ 6-u[/latex]
[latex]5u+10+14\ \textless \ 6-u[/latex]
[latex]5u+24\ \textless \ 6-u[/latex]
[latex]5u+u\ \textless \ 6-24[/latex]
[latex]6u\ \textless \ -18[/latex]
[latex]u\ \textless \ -3[/latex]
-------------(-3)-----------------
//////////////
[latex]u[/latex] ∈ [latex](-[/latex] ∞ [latex];-3)[/latex]
3)
[latex] \frac{1}{4} (3+8u) \geq 6,25+u[/latex]
[latex] \frac{3}{4} +2u \geq 6 \frac{1}{4} +u[/latex]
[latex]2u-u \geq 6 \frac{1}{4} - \frac{3}{4}[/latex]
[latex]u \geq 5 \frac{1}{2} [/latex]
------------[5.5]-----------------
//////////////////
[latex]u[/latex] ∈ [latex][5.5;+[/latex] ∞ [latex])[/latex]
4)
[latex]4(u+3)\ \textless \ 3(u+2)[/latex]
[latex]4u+12\ \textless \ 3u+6[/latex]
[latex]4u-3u\ \textless \ 6-12[/latex]
[latex]u\ \textless \ -6[/latex]
-------------(-6)-----------------
//////////////
[latex]u[/latex] ∈ [latex](-[/latex] ∞ [latex];-6)[/latex]
5)
[latex]3(2u+1)\ \textgreater \ 5(u-1)[/latex]
[latex]6u+3\ \textgreater \ 5u-5[/latex]
[latex]6u-5u\ \textgreater \ -5-3[/latex]
[latex]u\ \textgreater \ -8[/latex]
------------(-8)-----------------
//////////////////
[latex]u[/latex] ∈ [latex](-8;+[/latex] ∞ [latex])[/latex]
6)
[latex] \frac{3}{5} (5u- \frac{2}{3} )\ \textless \ u+7,6[/latex]
[latex]3u- \frac{2}{5}\ \textless \ u+7,6[/latex]
[latex]3u- 0.4\ \textless \ u+7,6[/latex]
[latex]3u-u\ \textless \ 7,6+0.4[/latex]
[latex]2u\ \textless \ 8[/latex]
[latex]u\ \textless \ 4[/latex]
-------------(4)-----------------
//////////////
[latex]u[/latex] ∈ [latex](-[/latex] ∞ [latex];4)[/latex]
Гость
1)
3-2и+2>8+и
3и<-3
и<-1
2)
5и+10+14<6-и
6и<-18
и<-3
3)
3/4+2и>=6,25+и
и>=5,5
4)
4и+12<3и+6
и<-6
5)
6и+3>5и-5
и>-8
6)
3и-2/5<и+7,6
2и<8
и<4
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