Odpowiedzi

2009-11-11T17:34:15+01:00
A) x+2/3 ≥ 3x-1/4
3x-x≤2/3+1/4
2x≤8/12+3/12
2x≤11/12 |*1/2
x≤11/24
x∈(-∞;11/24>

b) 25x²-(3-5x)² >15
25x²-(9-30x+25x²) >15
25x²-9+30x-25x² >15
30x>15+9
30x>24 | :30
x>24/30
x>4/5
x∈(4/5; +∞)

c) 6x²-(2x-3)(3x+2)<2
6x²-(6x²+4x-9x-6)<2
6x²-6x²-4x+9x+6<2
5x<2-6
5x<-4 |:5
x<-4/5
x∈(-∞; -4/5)
1 5 1
2009-11-11T17:42:02+01:00
1) x + 2/3 ≥ 3x - 1/4
x - 3x ≥ - 1/4 - 2/3
- 2x ≥ - 3/12 - 8/12
-2x ≥ - 11/12 / : (-2)
x ≤ 11/6
x ≥ 1 i 5/6


2) 25x² - (3-5x)² > 15
25x² - (3² - 2 razy 3 razy 5x + x²) > 15
25x² - (9 - 6x + 25x²) > 15
25x² - 9 + 6x - 25x² > 15
6x > 15 + 9
6x > 24 / : 6
x > 4



3) 6x² - (2x-3)(3x+2) < 2
6x² - (6x² + 4x - 9x - 6) < 2
6x² - 6x² - 4x + 9x + 6 < 2
5x < 2 - 6
5x < - 4 / :5
x < - 4/5