Question

Proporcje:Rozwiąż równania
1) 2/x=3/x-1
2)4/x+1=5/x
3)3/5=2x-1/2-5x
4)2x+1/1-2x=2/3
5)0,4-1/3=2x-5/2
6)4+x kwadrat/x=2x-1/2

Answer 1

1) 2/x=3/x-1
2(x-1)=3x
2x-2=3x
2x-2-3x=0
-x-2=0
-x=2/(-1)
x=-2


2)4/x+1=5/x
4x=5(x+1)
4x=5x+5
4x-5x-5=0
-x-5=0
-x=5/(-1)
x=-5


3)3/5=2x-1/2-5x
3(2-5x)=5(2x-1)
6-15x=10x-5
6-15x-10x+5=0
11-25x=0
11=25x/:25
11/25=x 4)2x+1/1-2x=2/3
2(1-2x)=3(2x+1)
2-4x=6x+3
2-4x-6x-3=0
-1=10x/:10
-1/10=x

Answer 2

1) 2/x=3/x-1
3x = 2(x-1)
3x = 2x-2
3x-2x = -2
x = -2

2)4/x+1=5/x
4x = 5(x+1)
4x = 5x+5
4x-5x = 5
-x = 5 |*(-1)
x = -5

3)3/5=2x-1/2-5x
3(2-5x) = 5(2x-1)
6-15x = 10x-5
-15x-10x = -5-6
-25x = -11 |:-25
x = 11/25
x = 0,44

4)2x+1/1-2x=2/3
2(1-2x) = 3(2x+1)
2-4x = 6x+3
-4x-6x = 3-2
-10x = 1 |:(-10)
x = -1/10
x = -0,1

5)0,4-1/3=2x-5/2
3(2x-5) = 2(0,4-1)
6x-15 = 4/5-2
6x = 15-2+0,8
6x = 13,8 |:6
x = 2,3

6)4+x kwadrat/x=2x-1/2
4+x²/x = 2x-1/2
2(4+x²) = x(2x-1)
8+2x² = 2x²-x
2x²-2x²+x = -8
x = -8