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2009-05-21T23:25:55+02:00
3x + 4(3-x)-(3x+2)=3
3x+12-4x-3x-2=3
-4x=3-10
-4x=-7
x=7/4
x=1 ¾

26x[22x-(30-3x)]=38
26x(22x-30+3x)=38
26x(25x-30)=38 /:2
13x(25x-30)=19
325x²-390x-19=0
Δ=(-390)²-4*325*(-19)=152100+24700=176800
√Δ=20√442
x₁=(390-20√442):650=(39-2√442):65
x₂=(390+20√442):650=(39+2√442):65


c)5(x-1)²-2(x-3)₂=3(x-2)₂-7(6x-1)
5(x²-2x+1)-2(x²-6x+9)=3(x²-4x+4)-42x+7
5x²-10x+5-2x²+12x-18=3x²-12x+12-42x+7
2x-13=-54x+19
56x=32
x=32/56
x=4/7

d)x+4/5 - x+5= x+3/3 - x-2/2 /*30
6(x+4)-30x+150=10(x+3)-15(x-2)
6x+24-30x+150=10x+30-15x+30
-24x+174=-5x+60
-19x=-114
x=6

e)6(2x+1)-(4+x)≥5(x-2)
12x+6-4-x≥5x-10
6x≥-12
x≥-2

f)(x-2)₂ + 3x < (x+2)₂ + 2x-3
x²-4x+4+3x<x²+4x+4+2x-3
-x+4<6x+1
-7x<-3
x>3/7


g) 5-4x/3 + x> -2x + 1/4 /*12
4(5-4x)+12x>-24x+3
20-16x+12x>-24x+3
20x>-17
x>-17/20
2009-05-21T23:29:12+02:00
A) 3x + 4(3-x)-(3x+2)=3
3x+12-4x-3x-2=3
-4x=3-10
-4x=-7
x=7/4
x=1 ¾

b) 26x[22x-(30-3x)]=38
26x(22x-30+3x)=38
26x(25x-30)=38 /:2
13x(25x-30)=19
325x²-390x-19=0
Δ=(-390)²-4*325*(-19)=152100+24700=176800
√Δ=20√442
x₁=(390-20√442):650=(39-2√442):65
x₂=(390+20√442):650=(39+2√442):65


c)5(x-1)²-2(x-3)₂=3(x-2)₂-7(6x-1)
5(x²-2x+1)-2(x²-6x+9)=3(x²-4x+4)-42x+7
5x²-10x+5-2x²+12x-18=3x²-12x+12-42x+7
2x-13=-54x+19
56x=32
x=32/56
x=4/7

d)x+4/5 - x+5= x+3/3 - x-2/2 /*30
6(x+4)-30x+150=10(x+3)-15(x-2)
6x+24-30x+150=10x+30-15x+30
-24x+174=-5x+60
-19x=-114
x=6

e)6(2x+1)-(4+x)≥5(x-2)
12x+6-4-x≥5x-10
6x≥-12
x≥-2

f)(x-2)₂ + 3x < (x+2)₂ + 2x-3
x²-4x+4+3x<x²+4x+4+2x-3
-x+4<6x+1
-7x<-3
x>3/7


g) 5-4x/3 + x> -2x + 1/4 /*12
4(5-4x)+12x>-24x+3
20-16x+12x>-24x+3
20x>-17
x>-17/20