Question

zad 2 str 207 matematyka z plusem 1 gimnazjum

proporcje:

a) 2/x = 3/x-1

b) 4/x+1 = 5/x

d)2x+1/1-2x = 2/3

e) 0,4x-1/3 = 2x-5/2

f) 4+x [do potęgi 2]/ x = 2x-1/2

Answer 1

a)2/x=3/x-1

2*(x-1)=3x

 2x-2=3x

-2=3x-2x

-2=x

b) 4/x+1=5/x

4x=5(x+1)

4x=5x+5

4x-5x=5

-x=5/:(-1)

x=-5

d)2x+1/1-2x=2/3

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

6x+3=2-4x

6x+4x=2-3

10x=-1/:10

x=-1/10

e)0,4x-1/3=2x-5/2

2(0,4x-1)=3*2x

0,8x-2=6x

0,8x-6x=2

-5,2x=2/:(-5,2)

x=-0,38461538

f)4+x2/x=2x-1/2

2(4+x2)=x(2x-1)

8+2x2=2x2-x

8=-x/(-1)

x=-8 

Answer 2

a) 2/x =  3/x-1

3x = 2(x-1)

3x = 2x – 2

3x-2x = -2

x = -2

 

 

b) 4/x+1 = 5/x

4x =5(x+1)

4x = 5x +5

4x -5x = 5

-x = 5    /* (-1)

x = -5

 

d)2x+1/1-2x  =  2/3

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

6x +3 = 2 – 4x

6x +4x = 2 -3

10x = -1  /: 10

x = -1/10

 

e) 0,4x-1/3  =  2x-5/2

2(0,4x-1) = 3(2x-5)

0,8x -2 = 6x -15

0,8x -6x = -15 +2

-5,2x = -13   / * (-10)

52x = 130   /:52

x = 130/52

x= 2 i 26/52

x = 2 i 1/2

 

f) 4+x²/ x  =  2x-1/2

2(4+x²) = x(2x-1)

8 + 2x² = 2x² -x

2x² -2x₂ -x = 8

-x = 8  /(-1)

x = -8