Question

Zad1 .

a)x/3 - 5/6 = 1/12 - x/2
b) 7/9 + x/2 = 3/2 - x/18
c)x/2 - 3/4 = 7/8 + x/4
d)x/9 + 1/2 = 5/4 = x/6 + 1/12

zad2.
a)0,7x-3+1,1x=-2,1+0,6
b)0,11x-0,08 + 0,4x =-0,01x+0,2
c)-0,4+2x-2,1=0,3x-0,8
d)0,06-1+0,4x=0,27-0,04x

zad3 .
a)x-1i1/2 - 1/3x=2+1/4x-5/6
b)3/10 - 1/2x +2/5=-1/5x+1i1/10+3/10x
c)5/7-2i1/14x-1i 1/2=2/7x-2
d)2x-3/4-1i1/5x=2/5-1/10
e)x/5-2/3+1i1/2=x/10-3/5-2x/3
f)1/20-3x/2+2i1/5=x/4=7/5

Answer 1

A) x/3-5/6=1/12-x/2 /*12
12*X/3-12*5/6=12*1/12-12*x/2
4x-10=1-6x
4x+6x=10+1
10x+11/:10
x=11/10=1,1/10

Answer 2

Zadanie 1
b)
7/9 + x/2 = 3/2 - x/18 /*18
14 + 9x = 27 - x
9x + x = 27 - 14
10x = 13 / : 10
x = 1,3 lub 1 i 3/10

c)
x/2 - 3/4 = 7/8 + x/4 /*8
4x - 6 = 7 + 2x
4x - 2x = 7 + 6
2x = 13 / :2
x = 7,5 lub 7 i 1/2

d)
x/9 + 1/2 = 5/4 - x/6 + 1/12 / * 36
4x + 18 = 45 - 6x + 3
4x + 6x = 45 + 3 - 18
10x = 30 / : 10
x = 3


zadanie 2
a)
0,7x - 3 + 1,1x = -2,1 + 0,6
7/10x - 3 + 1 i 1/10x = - 2 i 1/10 + 6/10
7/10x + 1 i 1/10x = -2 i 1/10 + 6/10 + 3
1 i 8/10x = -1 i 5/10 + 3
18/10x = 15/10 / : 18/10
x = 15/10 * 10/18
x = 15/18
x = 5/6

b)
0,11x - 0,08 + 0,4x = -0,01x + 0,2
11/100x - 8/100 + 4/10x = -1/100 + 2/10
11/100x + 40/100x = -1/100 + 20/100 + 8/100
51/100x = 27/100 / : 51/100
x = 27/100 * 100/51
x = 27/51

c)
-0,4 + 2x - 2,1 = 0,3x - 0,8
-4/10 + 2x - 2 i 1/10 = 3/10x - 8/10
20/10x - 3/10x = -8/10 + 21/10 + 4/10
17/10x = 17/10 / : 17/10
x = 17/10 * 10/17
x = 1

d)
0,06 - 1 + 0,4x = 0,27 - 0,04x
6/100 - 100/100 + 40/100x = 27/100 - 4/100x
40/100x + 4/100x = 27/100 + 100/100 - 6 /100
44/100x = 121/100 / : 44/100
x = 121/100 * 100/44
x = 121/44
x = 2 i 33/44
x = 2 i 3/4

zadanie 3
a)
x - 1 i 1/2 - 1/3 x = 2 + 1/4x - 5/6
x - 3/2 - 1/3 x = 2 + 1/4x - 5/6 / * 12
12x - 18 - 4x = 24 + 3x - 10
12x - 4x - 3x = 24 - 10 + 18
5x = 32 / : 5
x = 6 i 2/5

b)
3/10 - 1/2x + 2/5 = -1/5x + 1 i 1/10 + 3/10x
3/10 - 1/2x + 2/5 = -1/5x + 11/10 + 3/10x / * 10
3 - 5x + 4 = -2x + 11 +3x
- 5x + 2x - 3x = 11 - 4 - 3
- 6x = 4 / : (- 6)
x = (- 4/6)
x = (- 2/3)

c)
5/7 - 2 i 1/14x - 1 i 1/2 = 2/7x - 2
5/7 - 29/14x - 3/2 = 2/7x - 2 / * 14
10 - 29x - 21 = 4x - 28
-29x - 4x = -28 + 21 - 10
-33x = (- 17) / : (- 33)
x = 17/33

d)
2x - 3/4 - 1 i 1/5x = 2/5 - 1/10
2x - 3/4 - 6/5x = 2/5 - 1/10 / * 20
40x - 15 - 24x = 8 - 2
40x - 24x = 6 + 15
16 x = 21 / : 16
x = 21/16
x = 1 i 5/16

e)
x/5 - 2/3 + 1 i 1/2 = x/10 - 3/5 - 2x/3
x/5 - 2/3 + 3/2 = x/10 - 3/5 - 2x/3 / * 30
6x - 20 + 45 = 3x - 18 20x
6x - 3x + 20x = -18 + 20
23x = 2 / : 23
x = 2/23

f)
1/20 - 3x/2 + 2 i 1/5 = x/4 - 7/5
1/20 - 3x/2 + 11/5 = x/4 - 7/5 / * 20
1 - 30x + 44 = 5x - 28
-30x - 5x = -28 - 44 - 1
-35x = 73 / : (-35)
x = (- 73/35)
x - (- 2 i 3/35)