Question

Решите пожалуйста очень прошу:
(2x-1) (x+3)≥4

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Answer 1

$\displaystyle (2x-1)(x+3)\geq 4\\2x^2+6x-x-3\geq 4\\2x^2+5x-3\geq 4\\2x^2+5x-3-4\geq 0\\2x^2+7x-2x-7\geq 0\\x(2x+7)-(2x+7)\geq 0\\(2x+7)(x-1)\geq 0\\\\ \left \{ {{2x+7\geq 0} \atop {x-1\geq 0}} \right. \left \{ {{x\geq -\frac{7}{2} } \atop {x\geq 1}} \right. \\\\ \left \{ {{2x+7\leq 0} \atop {x-1\leq 0}} \right. \left \{ {{x\leq -\frac{7}{2} } \atop {x\leq 1}} \right. \\\\ x \in [1, +\infty), x\in (-\infty, - \frac{7}{2}]\\\\ x\in (-\infty, - \frac{7}{2}] \cup [1, +\infty)$