Question

TAKI ZNAK / TO KRESKA UŁAMKOWA

zad.1 Oblicz ile to x

a)1/2x - 4=x -6

b)x-5=1/3x+1

c)x/4-1/4=2

d)x/5-3=x+1/5

e)5/6 (x-1)=4

f)-1/2(-x-6)=-x

Zad.2 Rozwiąz równania

a)2x+3 2-x

--------- = ----- -x

5 3

b) x+1 x-1 1

------ - ---- = ---

2 3 4

c) 4x+7 5x-1

------- - -------- = x+5

2 6

d) x+5 2x+1 1

------ - ------- = -- (2-x)

4 8 2

Answer 1

zad. 1

a)

½x-4 = x-6   |*2 (mnożymy obustronnie przez 2 żeby pozbyć się ułamka)

x-8 = 2x-12

x-2x = -12+8

- x = -4

x = 4

 

b)

x-5 = ⅓x+1  |*3

3x-15 = x+3

3x-x = 3+15

2x = 18

x = 9

 

c)

x/4- ¼ = 2  |*4

x-1 = 8

x = 8+1

x = 9

 

d)

x/5-3 = x + ⅕  |*5

x-15 = 5x+1

x-5x = 1+16

-4x = 16

x = -4

 

e)

⅚(x-1) = 4

⅚x - ⅚ = 4  |*6

5x-5 = 24

5x = 24+5

x = 29/5 = 5⅘

 

f)

-½(-x-6) = -x

½x+3 = -x    |*2

x+6 = -2x

x+2x = -6

3x = -6

x = -2

 

zad. 2

a)

2x+3/5 = 2-x/3 -x        | *15

6x+9 = 10-5x-15x

6x+5x+15x = 10-9

26x = 1

x = 1/26

 

b)

x+1/2 - x-1/3 = ¼    |*12

6x+6-4x+4 = 3

2x = 3-6-4

2x = -7

x = -7/2

x = -3½

 

c)

4x+7/2- 5x-1/6 = x+5   I*6

3(4x+7) - (5x-1)= 6(x+5)

12x+2-5x+1 = 6x+30

7x - 6x= 30 - 22

x = 8

 

d)

x+5/4 - 2x+1/8 = ½(2-x)  |*8

2x+10-2x+1= 8-4x

2x-2x+4x = 8-10+1

4x = -1

x = -¼