Question

Rozwiąż nierówności
(2x-1)(2x+1)/4-(x+2)²≤x-5/2-6,25
(1-3x)²-x-5/3+2½<x+2/2+9(x+1)²-18x
(x-1)²/3-x+5/2>(⅓x-1)(x+6)-½
prosze

Answer 1

(2x-1)(2x+1)/4-(x+2)²≤x-5/2-6,25
4x do pot.2 - 2x - 2x + 1/4 - (x+2) (x+2) \< x - 5/2 - 6,25
4x do pot. 2 - 2x - 2x + 1/4 - x do pot.2 - 2x - 2x - 4 \< x - 5/2 - 6,25 | *4
4* 4x do pot 2 - 2x - 2x + 1/4 - 4x do pot. 2 - 8x - 8x - 16 \< 4x - 4*5/2 - 25
4x do po.2 - 2x - 2x + 1 - 4x do po.2 - 8x - 8x - 16 \< 4x - 10 - 25
-2x - 2x - 8x - 8x - 4x \< -10 - 25 + 16 - 1
-24x \< 18|:(-24)
x >/ -18/24 = -3/4

(1-3x)²-x-5/3+2½<x+2/2+9(x+1)²-18x
(1-3x) (1-3x) - x - 5/3 + 5/2 < x + 1 + 9 (x+1) (x+1) - 18x
1 - 3x - 3x + 9x do pot.2 - x - 5/3 + 5/2 < x + 1 + 9 (x do pot.2 + x + x + 1)- 18x
1 - 3x - 3x + 9xdo pot.2 - x - 5/3 + 5/2 < x + 1 + 9x do pot.2 + 9x +9x+9-18x|*6
6 - 18x - 18x + 54x do pot.2 - 6x - 6*5/3 + 6*5/2 < 6x + 6 + 54x do pot.2 + 54x + 54x + 108x
-18x - 18x + 54x do pot.2 - 6x - 6x - 54x do pot.2 - 54x - 54x - 108x < 54 + 6 - 15 + 10 - 6
264x < 51|: 264
x<51/264 = 17/88


(x-1)²/3-x+5/2>(⅓x-1)(x+6)-½
(x-1) (x-1)/3 - x + 5/2 > 1/3x do pot.2 + 6/3 - x - 6 - 1/2
x do pot.2 - x - x + 1/3 - x + 5/2 > 1/3 x do pot.2 + 2 - x - 6 - 1/2 |*6
6* x do pot.2 - x - x + 1 - 6x + ^*5/2 > 6*1/3x do pot.2 + `2 - 6x - 36 - 6*1/2
2(x do pot.2 - x - x + 1) - 6x + 15 > 2x do pot.2 + 12 - 6x - 36 - 3
2x do pot.2 - 2x - 2x + 1 - 6x + 15 > 2x do pot.2 + 12 - 6x - 36 - 3
2x do pot.2 - 2x - 2x - 6x - 2x do pot.2 + 6x > -3 - 36 + 12 - 15 - 1
-4x > 43\: (-4)
x < -43/4 = - 10 3/4

Answer 2

W zalaczniku jest rozwiazanie