Question

Rozwiąż równania:
a) 5x - 9 =1
b) 9x - 11 = 7x + 13
c) 26 - 3x = 2x + 41
d) 2(x + 5) = 5(x - 3)
e) -3(2x - 4) = 4(x + 5)
f) 2(3 - x) - 8x = 7(2x - 6
g) 4(2x - 1) + 9 = 16 - (8x + 3)

Answer 1

A)
5x - 9 =1

5x = 1 + 9

5x= 10

x= 10 : 5

x= 2


spr.
5x - 9 = 1

L = 5x - 9 = 5*2 - 9= 10 - 9 = 1

P = 1

1=1

L=P




b)
9x - 11 = 7x + 13

9x - 7x = 13 + 11

2x= 24

x= 24 : 2

x= 12


spr.
9x - 11 = 7x + 13

L = 9x - 11 = 9 * 12 - 11= 108 - 11= 97

P = 7x + 13= 7 * 12 + 13= 84 + 13= 97

97=97

L=P



c)
26 - 3x = 2x + 41

-3x - 2x= 41 - 26

- 5x = 15

x= 15 : (-5)

x= - 3


spr.
26 - 3x = 2x + 41

L = 26- 3x= 26 - 3*(-3)= 26 - (-9) = 26 + 9 = 35

P = 2x + 41= 2 * (-3) + 41= - 6 + 41= 35

35=35

L=P



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

2x + 2*5 = 5x - 5*3

2x + 10 = 5x - 15

2x - 5x= - 15 - 10

- 3x = - 25

x= - 25 : (-3)

x= 25/3

x= 8 i 1/3


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

L = 2(x + 5) = 2(8 i 1/3 + 5) = 2 * 13 i 1/3 = 2 * 40/3 = 80/3= 26 i 2/3

P= 5(x-3) = 5(8 i 1/3 - 3) = 5 * 5 i 1/3 = 5 * 16/3= 80/3= 26 i 2/3

26 i 2/3 = 26 i 2/3

L=P



e)
-3(2x - 4) = 4(x + 5)

-3*2x -4*(-3) = 4x + 4*5

- 6x -(-12) = 4x + 20

- 6x + 12 = 4x + 20

-6x - 4x= 20 - 12

- 10x = 8

x= 8 : (-10)

x= - 0,8


spr.
-3(2x - 4) = 4(x + 5)

L = - 3(2x - 4) = -6x + 12= -6 * (-0,8) + 12= 4,8 + 12= 16,8

P = 4(x + 5) = 4x + 20 = 4 * (-0,8) + 20 = - 3,2 + 20 = 16,8

16,8 = 16,8

L=P


f)
2(3 - x) - 8x = 7(2x - 6)

2*3 -2x - 8x = 7*2x - 7*6

6 - 10x = 14x - 42

-10x - 14x = - 42 - 6

- 24x = - 48

x= - 48 : (-24)

x= 2


spr.
2(3 - x) - 8x = 7(2x - 6)

L = 2(3-x) - 8x= 2(3-2) - 8*2= 2*1 - 16 = 2 - 16 = - 14

P = 7(2x-6) = 7(2*2 - 6) = 7(4-6) = 7 * (-2) = - 14

-14 = - 14

L =P



g)
4(2x - 1) + 9 = 16 - (8x + 3)

4*2x - 4*1 + 9 = 16 - 8x - 3

8x - 4 + 9 = - 8x +16 - 3

8x + 5= - 8x + 13

8x + 8x = 13 - 5

16x= 8

x= 8 : 16

x= 8/16

x= 0,5


spr.
4(2x - 1) + 9 = 16 - (8x + 3)

L = 4(2x - 1) + 9 = 4(2*0,5 - 1) + 9 = 4(1-1) + 9 = 4*0 + 9 = 0 + 9 = 9

P = 16 - (8x + 3) = 16 - (8 * 0,5 + 3) = 16 - (4 + 3) = 16 - 7 = 9

9 = 9

L=P

Answer 2

A) 5x-9=1
   5x=1+9
   5x=10/:5
    x=2

b) 9x-11=7x+13
   9x-7x=13+11
    2x=24/:2
    x=12

c) 26-3x=2x+41
   -3x-2x=41-26
    -5x=15/:(-5)
      x=-3

d) 2(x+5)=5(x-3)
    2x+10=5x-15
    2x-5x=-15-10
    -3x=-25/:(-3)
       x=25/3=8 1/3

e) -3(2x-4)=4(x+5)
    -6x+12=4x+20
    -6x-4x=20-12
     -10x=8/:(-10)
       x=-8/10=-4/5

f) 2(3-x)-8x=7(2x-6)
   6-2x-8x=14x-42
    -2x-8x-14x=-42-6
     -24x=-48/:(-24)
      x=2

g) 4(2x-1)+9=16-(8x+3)
     8x-4+9=16-8x-3
     8x+8x=16-3+4-9
     16x=8/:16
      x=8/16=1/2