Question

Rozwiąż równania
a 4-(2x-5)<x-(5+3x)
c (x-3)/2-(x+3)/4<1/4(x+2)
b 7(x-3)+5(4-x)>4(2x-1)-2(3x+2)
d (x-1)/3-(2x+5)/6>=1
e (x-1)do kwadratu-(x+2)<=3(1-2x)
f (x-3)(x+3)-6(x-3)<=(4-x)do kwadratu+2(x-5)

Answer 1

A 4-(2x-5)<x-(5+3x)
-2x-1<-2x-5
0<-4
c (x-3)/2-(x+3)/4<1/4(x+2) //*4
2x-6-x-3<x+2
0<11
b 7(x-3)+5(4-x)>4(2x-1)-2(3x+2)
7x-21+20-5x>8x-4-6x-4
2x-1>2x-8
0>-7
d (x-1)/3-(2x+5)/6>=1 //*6
2x-2-2x+5>-1
0>-4
e (x-1)do kwadratu-(x+2)<=3(1-2x)
x²-2x+1-x-2<-3-6x
x²--3x-1<-3-6x
x²+3x<-2
x²-3x+2<0
Δ=b²-4ac=9-8=1
x1=-b-√Δ/2a=3-1/2=2-2=1
x2=-b+√Δ/2a=3+1/2=4/2=2
(x-1)(x-2)<0 <=> x<1 lub x<2
f (x-3)(x+3)-6(x-3)<=(4-x)do kwadratu+2(x-5)
x²+3x-3x-9-6x+18<16-8x+x²+2x-10
-6x+9<6-6x
0<-3