Question

Rozwiąż równania i sprawdź:

a) 1/2x -3= 1/4x +1

b) 1/2 (x-2)= -x- 1/2 (x-8)

c) x-1 /2= x+1

d) x+3 /3 +1=4-x/6

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

f) x+2 /3 + 2x+1 / 2=1

Answer 1

Rozwiąż równania i sprawdź:

a) 1/2x -3= 1/4x +1  /*4

2x-12=x+4

2x-x=4+12

x=16

spr

1/2 * 16-3=1/4 *16+1

5=5

L=P

 

b) 1/2 (x-2)= -x- 1/2 (x-8) /*2

x-2=-2x-x+8

4x=10 /:4

x=10/4 = 2 1/2

spr

1/2(10/4-2)=-10/4-1/2(10/4-8)

1/2*1/2=-10/4-1/2*(-22/4)

1/4=-10/4+11/4

1/4=1/4

L=P

 

c) (x-1) /2= x+1  /*2

x-1=2x+2

-x=3 /*(-1)

x=-3

spr

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

-2=-2

L=P

 

d) (x+3) /3 +1=(4-x)/6   /*6

2(x+3)+6=4-x

2x+6+6=4-x

3x=-8  /:3

x=-8/3

spr

(-8/3 +3) /3 +1 = (4+8/3)/6

1/3*1/3+1=20/3 *1/6

1 1/9= 20/18

10/9=10/9

L=P

 

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

4x-1 1/4=0

4x=5/4  /:4

x=5/16

spr

5*5/16+1/4-1-5/16-1/2=0

25/16+4/16-1-5/16-8/18=0

16/16-1=0

0=0

L=P

 

f) x+2 /3 + 2x+1 / 2=1  /*6

6x+4+12x+3=6

18x=-1 /:18

x=-1/18

spr

-1/18+2/3+2*(-1/18)+1/2=1

-1/18+12/18-2/18+9/18=1

18/18=1

L=P

Answer 2

·a)1/2x-3=1/4x+1

2x-12=x+4

2x-x=12+4

x=16

spr.   8-3=4+1

         5=5

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b)1/2(x-2)=-x-1/2(x-8)

1/2x-1=-x-1/2x+4

2x=4+1

2x=5

x= 2 1/2

spr.  1/2·1/2=-5/2-1/2·(-5 1/2)

        1/4=-5/2-1/2·(-11/2)

        1/4=-5/2+11/4

       1/4=-10/4+11/4

        1/4=1/4

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c) x-1/2=x+1   mnozymy przez 2

2x-1=2x+2

-1=2        rownanie sprzeczne, nie ma rozwiazan

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e)5x+1/4-1-x-1/2=0    mnozymy przez4

20x+1-4-4x-2=0

16x=5

x=5/16

spr      25/16+1/4-1-5/16-8/16=0

          25/16+4/16-1-13/16=0

         0=0

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x+2/3+2x+1/2=1   mnozymy przez 6

6x+4+12x+3=6

18x=6-7

18x=-1

x=-1/18

spr    -1/18+12/18-2/18+9/18=1

   1=1

3x+2