Question

1да Вопрос:
Решите двойное неравенство:
-6 <2x +1 <0
знак <=с черточкой внизу.
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Answer 1

Решить можно двумя :

первый  ⇒

$-6\leq 2x+1\leq 0\\\\-6-1\leq 2x+1-1\leq 0-1\\\\-7\leq 2x\leq -1\\\\-7:2\leq 2x:2\leq -1:2\\\\-3,5\leq x\leq-0,5\\\\x\geq -3,5\\\\x\leq -0,5$

x ∈ [ -3,5 ; 0,5 ]

второй  ⇒

$-6\leq 2x+1\leq 0\\\\\left \{ {{2x+1\geq -6} \atop {2x+1\leq 0}} \right. \\\\\left \{ {{2x\geq -6-1} \atop {2x\leq 0-1}} \right. \\\\\left \{ {{2x\geq -7} \atop {2x\leq -1}} \right. \\\\\left \{ {{x\geq -7:2} \atop {x\leq-1:2 }} \right. \\\\\left \{ {{x\geq -3,5} \atop {x\leq -0,5}} \right.$

x ∈ [ -3,5 ; 0,5 ]