Question

1. Rozwiąż i sprawdź następujące równania:

a) 2(x+2)-3(x-1)+8=3x-1

b) 4x-3(x+7)-5x+2(x-1)=9

c) 1/2x-7=x-36/3

d) 5x(x-2)-x(5x-2)=-4

e) x(2-x)=(x+2)(x-2)=2

f) (2x-3)(2x+3)-4x(x+2)+49=-4x

Answer 1

a) 2(x+2)-3(x-1)+8=3x-1

2x+4-3x+3+8 = 3x-1

2x-3x-3x = -1-4-3-8

-4x = -16 |:(-4)

x = 4

 

spr.

2*(4+2)-3*(4-1)+8 = 3*4-1

2*6-3*3+8 = 12-1

12-9+8 = 11

11 = 11

 

 

b) 4x-3(x+7)-5x+2(x-1)=9

4x-3x-21-5x+2x-2 = 9

4x-3x-5x+2x = 9+21+2

-2x = 32 |:(-2)

x = -16

 

spr.

4*(-16)-3*(-16+7)-5*(-16)+2*(-16-1) = 9

-64-3*(-9)+80+2*(-17) = 9

-64+27+80-34 = 9

9 = 9

 

 

c) 1/2x-7=x-36/3 |*6

3x-42 = 2x-72

3x-2x = -72+42

x = -30

 

spr.

1/2*(-30)-7 = -30-36 / 3

-15-7 = -66/3

-22 = -22

 

 

d) 5x(x-2)-x(5x-2)=-4

5x²-10x-5x²+2x = -4

-10x+2x = -4

-8x = -4 |:(-8)

x = 1/2

 

spr.

5*1/2*(1/2-2)-1/2*(5*1/2-2) = -4

5/2 * (-3/2)-1/2*(5/2-2) = -4

-15/4-1/2*1/2 = -4

-15/4-1/4 = -4

-16/4 = -4

-4 = -4

 

 

e) x(2-x)+(x+2)(x-2)=2

2x-x²+ x²-4 = 2

2x = 2+4

2x = 6 |:2

x = 3

 

spr.

3*(2-3)+(3+2)*(3-2) = 2

3*(-1)+5*1 = 2

-3+5 = 2

2 = 2

 

f) (2x-3)(2x+3)-4x(x+2)+49=-4x

4x²-9-4x²-8x+49 = -4x

-8x+4x = 9-49

-4x = -40 |:(-4)

x = 10

 

spr.

(2*10-3)(2*10+3)-4*10*(10+2)+49 = -4*10

(20-3)*(20+3)-40*12+49 = -40

17*23-480+49 = -40

391-480+49 = -40

-40 = -40