Question

1.Rozwiąż równania:

a) -7(x+2)+4= -3

b) 1- 2x+5:3 = 4

2.Rozwiąż równania podane w postaci proporcji:

a) x/2 = 5/6

b) x/2 = x+1:4

c)2(x-1):3 = x+2:5

d) x-1: x+3 = x:x+1

Answer 1

1.Rozwiąż równania:

a) -7(x+2)+4= -3

 -7x -14 +4 = -3

  -7x -10 = -3

  -7x = -3 +10

  -7x = 7

     x = 7 : (-7)

     x = -1

 

b) 1- 2x+5:3 = 4

     1 -2x + 5/3 = 4        /*3

      3 -6x +5 = 12

         -6x +8 = 12

         -6x = 12-8

         -6x = 4

            x = 4 : (-6)

            x = - 2/3

      

 

2.Rozwiąż równania podane w postaci proporcji:

 

b) x/2 = x+1:4

 4x = 2(x+1)

 4x = 2x +2

 4x -2x = 2

  2x = 2

   x = 2 :2

   x = 1

 

c)2(x-1):3 = x+2:5

5*2(x-1) = 3(x+2)

 10x -10 = 3x +6

  10x -3x = 6 +10

    7x = 16

      x = 16 :7

      x = 16/7

      x = 2 i 2/7

 

d) x-1: x+3 = x:x+1

 (x-1)*(x+1) = x(x+3)

 x² -1 = x² +3x

 x² -x² -3x = 1

          -3x = 1

           x = 1 : (-3)

          x = -1/3

 

Answer 2

1.

a) -7(x+2)+4= -3

-7x-14+4=-3

-7x=-3+10

-7x=7

x=1

 

b) - 2x+5:3 = 4    /*3 (cąłość mnozymy razy 3)

-1-2x+5=12

-2x=8

x=-4

 

2.

a) x/2 = 5/6

6x=10

x=5/3

 

b) x/2 = x+1:4

2(x+1)=4x

2x+2=4x

2x-4x=-2

-2x=-2

x=1

c)2(x-1):3 = x+2:5

5(2x-2)=3(x+2)

10x-10=3x+6

10x-3x=6+10

7x=16

x=2

d) x-1: x+3 = x:x+1

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

x²+3x=x²-1

x=