a) 1 intreg 1/2=(1x2+1)/2=3/2
x/6=3/2·(2/3-x/2) aducem paranteza la acelasi numitor
x/6=3/2·[(2·3-3x)/6]
x/6=3/2·(6-3x)/6 simplif.cu 3
x/6=1/2·(6-3x)/2
x/6=(6-3x)/4
4x=6(6-3x)
4x=36-18x
4x+18x=36
22x=36
x=36/22 simplif cu 2
x=18/11
b)
1 intreg 3/5=(1·5+3)/5=8/5
x/5=8/5·(5/8-x/3)
x/5=8/5·[(5·3-8x)/24] simplif cu 8
x/5=1/5·(15-8x)/3
x/5=(15-8x)/15
15x=5(15-8x)
15x=75-40x
15x+40x=75
55x=75
x=75/55 simplif cu 5
x=15/11
c)x/3=7/4·(4/7-x/2)
x/3=7/4·[(4·2-7x)/14]
x/3=1/4·(8-7x)/2
x/3=(8-7x)/8
8x=3(8-7x)
8x=24-21x
8x+21x=24
29x=24
x=24/29
d) (11x/6-7/4)·4/3=8x/9
[(11x·2-7·3)/12]·4/3=8x/9
[(22x-21)/12]·4/3=8x/9
simplif
[(22x-21)/3]·1/3=8x/9
(22x-21)/9=8x/9
22x-21=8x
22x-8x=21
14x=21
x=21/14 simplif
x=3/2
e) (10x/9-7/6)·2/5=x/5
[(10x·2-7·3)/18]·2/5=x/5 simplif
[(20x-21)/9]·1/5=x/5
(20x-21)/45=x/5
5(20x-21)=45x
100x-105=45x
100x-45x=105
55x=105
x=105/55 simplif
x=21/11
f) (6x/5-7/8)·4/9=2x/9
[(6x·8-7·5)/40]·4/9=2x/9
[(48x-35)/10]·1/9=2x/9
(48x-35)/90=2x/9
9(48x-35)=2x·90
432x-315=180x
432x-180x=315
252x=315
x=315/252
x=105/84
x=35/28
