Question

Решите двойное неравенство: 1)-2< 3x+1< 7; 3) 4< 7-4x< 15 2)2< 5x-3< 27; 4)-12< 2(x+3)< 4

Answer 1

Разобьем каждое двойное неравенство на систему неравенств, решаем систему, собираем ответ в двойное неравенство:
1. $\left \{ {3x+1\ \textgreater \ -2} \atop {3x+1\ \textless \ 7}} \right.$
$\left \{ {3x\ \textgreater \ -3} \atop {3x\ \textless \ 6}} \right.$
$\left \{ {x\ \textgreater \ -1} \atop {x\ \textless \ 2}} \right.$
$-1\ \textless \ x\ \textless \ 2$

2. $\left \{ {{5x-3\ \textgreater \ 2} \atop {5x-3\ \textless \ 27}} \right.$
$\left \{ {{5x\ \textgreater \ 5} \atop {5x\ \textless \ 30}} \right.$
$\left \{ {{x\ \textgreater \ 1} \atop {x\ \textless \ 6}} \right.$
$1\ \textless \ x\ \textless \ 6$

3. $\left \{ {{7-4x\ \textgreater \ 4} \atop {7-4x\ \textless \ 15}} \right.$
$\left \{ {{-4x\ \textgreater \ -3} \atop {-4x\ \textless \ 8}} \right.$
$\left \{ {{x\ \textless \ \frac{3}{4} } \atop {x\ \textgreater \ -2}} \right.$
$-2\ \textless \ x\ \textless \ frac{3}{4}$

4. $\left \{ {2(x+3)\ \textgreater \ -12} \atop {2(x+3)\ \textless \ 4}} \right.$
$\left \{ {2x+6\ \textgreater \ -12} \atop {2x+6\ \textless \ 4}} \right.$
$\left \{ {2x\ \textgreater \ -18} \atop {2x\ \textless \ -2}} \right.$
$\left \{ {x\ \textgreater \ -9} \atop {x\ \textless \ -1}} \right.$
$-9\ \textless \ x\ \textless \ -1$

Answer 2

Вот, надеюсь понятно .. Сверху 4,3 снизу 1,2