6х-1

August 2022 1 25 Report

50 Б РЕШИТЬ НЕРАВЕНСТВО (х+5)(х-6)/6х-1<=0

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(x²-6x+5x-30-6x)/6x≤0
(x²-7x-30)/6x≤0
x²-7x-30=0
x1+x2=7 U x1*x2=-30
x1=-3 U x2=10
6x=0
x=0
_ + _ +
------------------[-3]-----------(0)------------[10]------------------
x∈(-∞;-3[ U (0;10]
______________________________________
(x+5)(x-6)/(6x-1)≤0
x=-5 x=6 x=1/6
_ + _ +
------------------[-5]-----------(1/6)------------[6]------------------
x∈(-∞;-5} U (1/6;6]

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