a)
(x+5)/(x-7)=0 , dla x-7≠0 ⇔ x≠7
x+5=0
x=-5
x ∈ {-5}
b)
(3x+2)/(x+2)=2 , dla x+2≠0 ⇔ x≠-2
3x+2=2(x+2)
3x+2=2x+4
3x-2x=4-2
x=2
x ∈ {2}
c)
5x/(4x-7) < 2 , dla 4x-7≠0 ⇔ x≠7/4
5x/(4x-7)-2 < 0
5x/(4x-7)-2(4x-7)/(4x-7) < 0
5x/(4x-7)-(8x-14)/(4x-7) < 0
[5x-(8x-14)/(4x-7) < 0
(5x-8x+14)/(4x-7) < 0
(-3x+14)/(4x-7) < 0
-(3x-14)/(4x-7) < 0 |:(-1)
(3x-14)/(4x-7) > 0
(3x-14)(4x-7) > 0
3x-14=0 ∨ 4x-7=0
3x=14 |:3 ∨ 4x=7|:4
x=14/3 ∨ x=7/4
x ∈(-∞,7/4)∪(14/3,∞)
d)
3/(2x-1) < 0 , dla 2x-1≠0 ⇔ x≠1/2
3(2x-1) < 0|:3
2x-1 < 0
2x < 1 |:2
x < 1/2
x∈ (-∞,1/2)
