Question

Rozwiąż równania.
a)(x-3)(5-x)-2=(2-x)(x-4)+3
b)(6-x)(x+2)+(x+3)(x-4)=2x+5
c)(x-5)(x+2)-(3-x)(2-x)=x-12
d)(2x-5)(x+1)-2=(1-x)(8-2x)+2x

Answer 1

a)

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

5x - x² - 15 + 3x - 2 = 2x - 8 - x² + 4x + 3

- x² + 8x - 17 = - x² + 6x - 5

- x² + 8x  + x² - 6x = - 5 + 17

2x = 12 /:2

x = 6

b)

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

6x + 12 - x² - 2x + x² - 4x + 3x - 12 = 2x + 5

3x = 2x + 5

3x - 2x = 5

x = 5

c)

(x - 5)(x + 2) - (3 - x)(2 - x) = x - 12

x² + 2x - 5x - 10 - (6 - 3x - 2x + x²) = x - 12

x² - 3x - 10 - (6 - 5x + x²) = x - 12

x² - 3x - 10 - 6 + 5x - x² = x - 12

2x - 16 = x - 12

2x - x = - 12 + 16

x = 4

d)

(2x - 5)(x + 1) - 2 = (1 - x)(8 - 2x) + 2x

2x² + 2x - 5x - 5 - 2 = 8 - 2x - 8x + 2x² + 2x

2x² - 3x - 7 = 2x² - 8x + 8

2x² - 3x -  2x² + 8x = 8 + 7

5x = 15 /:5

x = 3

 

 

Answer 2

a)

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

5x - x² - 15 + 3x - 2 = 2x - 8 - x² + 4x + 3

8x - 17 = 6x - 5

8x - 6x = - 5 + 17

2x = 12

x = 12 : 2

x = 6

b)

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

6x + 12 - x² - 2x + x² - 4x + 3x - 12 = 2x + 5

6x - 2x - 4x + 3x = 2x + 5

3x = 2x + 5

3x - 2x = 5

x = 5

c)

(x - 5)(x + 2) - (3 - x)(2 - x) = x - 12

x² + 2x - 5x - 10 - (6 - 3x - 2x + x²) = x - 12

x² - 3x - 10 - 6 + 5x - x² = x - 12

2x - 16 = x - 12

2x - x = 16 - 12

x = 4

d)

(2x - 5)(x + 1) - 2 = (1 - x)(8 - 2x) + 2x

2x² + 2x - 5x - 5 - 2 = 8 - 2x - 8x + 2x² + 2x

- 3x - 7 = - 8x + 8

- 3x + 8x = 8 + 7

5x = 15

x = 15 : 5

x = 3