Question

11. Rozwiąż równania

a) 2x+3/5 = 2-x/3 - x
b) x+1/2 - x-1/3 = 1/4
c) 4x+7/2 - 5x-1/6 = x + 5
d) x+5/4 - 2x+1/8 = 1/2(2 - x)

Answer 1

a) 2x+3/5 = 2-x/3 - x / * 15

30 x + 9 = 30 - 5 x - 15 x

30 x + 5 x + 15 x = 21

50 x = 21 / : 50

x = 21/50 = 0,02

x = 0,412

 

b) x+1/2 - x-1/3 = 1/4 / * 12

12 + 6 - 12 x - 4 = 3

-12 x = 3 - 12 - 6 + 4

-12 x = - 11 / : (-12)

x = 11/12 = 0,92

x = 0,92

 

c) 4x+7/2 - 5x-1/6 = x + 5 / * 6

24 x + 21 - 30 x - 1 = 6x + 30

24 x - 30 x - 6 x = 30-21 + 1

-12 x = 10 / : (-12)

x = - 10/12 = -5/6

 

d) x+5/4 - 2x+1/8 = 1/2(2 - x)

x  + 5/4 - 2 x + 1/8 = 1 - 1/2 x / * 8

8 x + 10 - 16 x + 1 -= 8 - 4 x

8 x - 16 x + 4x = 8 - 10- 1

- 4 x = -3 / (-4)

x = 3/4

Answer 2

a) 2x+3/5 = 2 - x/3 - x /*15

30x+9= 30 - 5x - 15x

30 x+20 x = 30 -9

50 x = 21/:50

x = 21/50

 

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

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

0 = 3/12 - 6/12 +4/12

0 = 1/12

 

c) 4x + 7/2 -5x -1/6 = x +5

4x -5x - x = 5 -7/2 +1/6

- 2x = 5 -3 i 1/2 +1/6

- 2x = 5 -3 i 3/6 + 1/6

-2x = 4 i 7/6 - 3 i 3/6

- 2x = 1 i 4/6

-2x = 1 i 2/3

- 2x = 5/3  /:(-2)

x = -  5/3*1/2

x = - 5/6

 

d) x + 5/4 -2x + 1/8 = 1 - 1/2x

x - 2x +1/2x = 1 -5/4 -1/8

- 1/2 x = 1 -10/8 - 1/8

-1/2x = -3/8

x = 3/8 * 2/1

x = 6/8

x = 3/4