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

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    

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

Sprawdzian z matematyki ,,Równania i Nierówności'

grupa A (22 pkt)

Zad. 1. (4 pkt) Rozwiąż równania.
a) 3(y+6) + y = 2(y+9) + 2
b) frac{5(x-1)}{3}-frac{3(2x-3)}{2}=2frac{1}{2}-x

Zad. 2. (3 pkt) Rozwiąż nierówność frac{3x-5}{7}+frac{7-5x}{14}leqfrac{x-1}{2}-1 i prze...