Question

Розв'язати нерівність

Answer 1

Ответ:

1)2x-1/x-4<1/2

2x-1/x-4-1/2<0

2(2x-1)-(x-4)/2(x-4)<0

4x-2-x+4/2(x-4)<0

3x+2/2(x-4)<0

$\left \{ {{3x+2<0} \atop {2(x-4)>0}} \right.$

$\left \{ {{x<-2/3} \atop {x>4}} \right.$

x∈∅

x∈(-2/3,4)

2) 18-x/x-5>-3

18-x/x-5+3>0

18-x+3x(x-5)/x-5>0

18-x+3x-15/x-5>0

3+2/x-5>0

$\left \{ {{3+2x>0} \atop {x-5>0}} \right.$

$\left \{ {{x>-3/2} \atop {x>5}} \right.$

x∈(5,+∞)

x∈(-∞,-3/2)

x∈(-∞,-3/2)∪(5,+∞)

3)9x+14/x+5≤4

9x+14/x+5-4≤0

9x+14-4(x+5)/(x+5)≤0

9x+14-4x-20/(x+5)≤0

5x-6/x+5≤0

$\left \{ {{5x-6≤0} \atop {x+5>0}} \right.$

$\left \{ {{x}≤6/5 \atop {x>-5}} \right.$

x∈(-5,6/5] ,x≠-5

x∈∅

x∈(-5,6/5]