Question

Rozwiąż równania :

a) 2/3x - 5 = 1 - 1/3x

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

c) 5 ( 1 - 2x) - 4x = -7

d) 1i1/2x - 1/4 = 3i1/2 - 3/4x

e) x-1/3 + 5/12 = 2 - 1/4x

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

Answer 1

a) 2/3x - 5 = 1 - 1/3x    /*3
2x - 15 = 3 - x
2x + x = 3 + 15
3x = 18    /:3
x = 6

b) 2x - ( 3 - x ) = 5 + 2x
2x - 3 + x = 5 + 2x
2x + x - 2x = 5 + 3
x = 8

c) 5( 1 - 2x) - 4x = -7
5 - 10x - 4x = -7
-10x - 4x = -7 - 5
-14x = -12   /:(-14)
x = 6/7

d) 1i1/2x - 1/4 = 3i1/2 - 3/4x
3/2x - 1/4 = 7/2 - 3/4x     /*4
6x - 1 = 14 - 3x
6x + 3x = 14 + 1
9x = 15    /:9
x = 5/3

e) x-1/3 + 5/12 = 2 - 1/4x   /*12
12x - 4 + 5 = 24 - 3x
12x + 3x = 24 + 4 - 5
15x = 23    /:15
x = 23/15

f) 0,3( 5 - 2x ) = 2 - 0,4( x + 1 )
1,5 - 0,6x = 2 - 0,4x - 0,4
-0,6x + 0,4x = 2 - 0,4 - 1,5
-0,2x = 0,1   /:(-0,2)
x = -0,5

Answer 2

a)

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

b)

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

2x-3+x=5+2x

x = 8

 

c)

5 ( 1 - 2x) - 4x = -7

5 - 10x - 4x = -7

-14x = -12   /: (-14

x = 12/14 = 6/7

 

d)

1i1/2x - 1/4 = 3i1/2 - 3/4x

6/4x + 3/4x = 14/4+1/4

9/4x = 15/4   /*4/9

x = 15/9 = 1 6/9 = 1 2/3

 

e)

x-1/3 + 5/12 = 2 - 1/4x

x+1/4x = 2-5/12+1/3

5/4x = 24/12-5/12+4/12

5/4x = 23/12   /* 4/5

x = 23/15 = 1 8/15

 

f)

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

1,5-0,6x = 2 - 0,4x - 0,4

-0,2x = 2-0,4-1,5

-0,2x = 0,1   /:(-0,2

x =- 0,5