[tex] \frac{2- (x-5)^{-1} }{2(x-5)^{-1}-1} \geq -1[/tex]. Created by Sadikta. algebra-ru

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Sadikta @Sadikta

July 2022 1 13 Report

[tex] \frac{2- (x-5)^{-1} }{2(x-5)^{-1}-1} \geq -1[/tex]

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Universalka

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$\frac{2-(x-5) ^{-1} }{2(x-5) ^{-1}-1 } \geq -1\\\\ \frac{2- \frac{1}{x-5} }{ \frac{2}{x-5} -1} \geq -1\\\\ \frac{ \frac{2x-10-1}{x-5} }{ \frac{2-x+5}{x-5} } \geq -1\\\\ \frac{2x-11}{7-x} +1 \geq 0\\\\ \frac{2x-11+7-x}{7-x} \geq 0\\\\ \frac{x-4}{7-x} \geq 0$
Заменим частное произведением, учитывая что 7 - x ≠ 0    ⇒ x ≠ 7
(x - 4)(7 - x) ≥ 0
(x - 4)(x - 7) ≤ 0
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            4                       7
x ∈ [4 ; 7)

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