Question

Решите двойное неравенство, подробно, пожалуйста !!!!! (9 класс)
$- 3 \leqslant 1 - \frac{y - 3}{2} \leqslant 4$
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Answer 1

Ответ:

Объяснение:

$\displaystyle-3\leq 1-\frac{y-3}{2} \leq 4\\\\\left \{ {{-3\leq1-\dfrac{y-3}{2} } \atop {1-\dfrac{y-3}{2}}\leq 4} \right.$

умножим на 2

$\displaystyle\\\left \{ {{-6\leq 2-(y-3)} \atop {2-(y-3)\leq 8}} \right. \ \ \ \left \{ {{-6\leq 2-y+3} \atop {2-y+3\leq 8}} \right. \ \ \ \left \{ {{-6\leq 5-y} \atop {5-y\leq 8}} \right.\\\\\\\left \{ {{y\leq5+6 } \atop {y\geq 5-8}} \right.\ \ \ \left \{ {{y\leq 11} \atop {y\geq -3}} \right. \ \ \ \ \ =>-3\leq y\leq 11\\\\\\Otvet:y\in[-3;11]$