Question

1 Rezolvati in Q ecuatiile:
a) 5/6x : 1 intreg si 1/2=0,25
b) 11/15: x =22/5
c) 2 intregi si 3/4:x=33/8
d) 5 intregi si 1/4:2x =6 intregi si 1/8

2 Rezolvati in Q ecuatiile:
a) 2(x+1/5)=1 intreg si 3/4
b) 1/4(x+6/7)=5/7
c) 0,5(x+2/9)=0,75
d) 3/5(x-1/2)=6
e) 0,(2)·(3x₋0,75)=1/3
f)  1/7(x₋0,(23) )=5/14
g) 3,75(x₋0,(3) )=5/14
h) 1,(3) · (3x₋ 0,75)=1/3
i)   5/7(4x₋0,6(3) )=10/21
VA ROG OFER 20 PUNCTE

Answer 1

a) 5/6x : 1 intreg si 1/2=0,25
5/6x:3/2=25/100
5/6x·2/3=25/100
10/18x=25/100 simplif
5/9x=1/4
5·4=9x
9x=20
x=20/9
b) 11/15: x =22/5
11/15·1/x=22/5
11/15x=22/5
11·5=22·15x
330x=55
x=55/330=simplif cu 11=5/30=1/6
c) 2 intregi si 3/4:x=33/8
11/4·1/x=33/8
11/4x=22/8
11·8=22·4x
88x=88
x=88/88
x=1
d) 5 intregi si 1/4:2x =6 intregi si 1/8
21/4·1/2x=49/8
21/8x=49/8
21·8=49·8x
392x=168
x=168/392=81/196

2 
a) 2(x+1/5)=1 intreg si 3/4
2x+2/5=7/4
2x=7/4-2/5
2x=(35-8)/20
2x=27/20
x=27/2·20=27/40
b) 1/4(x+6/7)=5/7
x/4+6/28=5/7
x/4=5/7-6/28
x/4=(20-6)/28
x/4=14/28 simplif
x/4=1/2
2x=4
x=4/2
x=2
c) 0,5(x+2/9)=0,75
5/10(x+2/9)=75/100 simplif
5x/10+10/90=15/20 simplif
x/2+1/9=3/4
x/2=3/4-1/9
x/2=(27-4)/36
x/2=23/36
x=23·2/36 simplif
x=23/18
d) 3/5(x-1/2)=6
3x/5-3/10=6
3x/5=6/1+3/10
3x/5=(60+3)/10
3x/5=63/10
10·3x=63·5
x=315/30 simplif
x=63/6 simplif
x=21/2
e) 0,(2)·(3x₋0,75)=1/3
2/10(3x-75/100)=1/3   simplif
1/5(3x-3/4)=1/33
x/5-3/20=1/33
x/5=1/3+3/203
x/5=(20+9)/603
x/5=29/603
x·60=29·5
180x=145
x=145/180 simplif
x=29/36
f) 1/7(x₋0,(23) )=5/14
1/7(x-23/9)=5/14
x/7-23/63=5/14
x/7=5/14+23/6
3x/7=(45+46)/126
x/7=91/126
126x=91·7
x=639/126 simplif
x=213/42 simplif
x=71/14
g) 3,75(x₋0,(3) )=5/14
375/100(x-3/9)=5/14 simplif
75/20(x-1/3)=5/14   simplif
15/4(x-1/3)=5/14
15x/4-15/12=5/14
15x/4=5/14+15/12
15x/4=(60+210)/168
15x/4=270/168 simplif
15x/4=90/56
15x·56=90·4
840x=360
x=360/840
x=36/84 simplid
x=18/42 simplif
x=9/21 simplif
x=3/7

h) 1,(3) · (3x₋ 0,75)=1/3
(13-1)/9·(3x-75/100)=1/3  simplif
12/9(3x-15/20)=1/3 simplif
4/3(3x-3/4)=1/3
12x/3-12/12=1/3
4x-1=1/3
4x=1/3+1
4x=(1+3)/3
4x=4/3
12x=4
x=4/12 simplif
x=1/3
i) 5/7(4x₋0,6(3) )=10/21
5/7(4x-(63-6)/90)=10/21
5/7(4x-57/90)=10/21 simplif
5/7(4x-19/30)=10/21
20x/7-95/210=10/21
20x/7=10/21+95/210
20x/7=(100+95)/210
20x/7=195/210   simplif
20x/7=65/70   simplif
20x/7=13/14
20x·14=13·7
280x=91
x=91/280

Answer 2

1.
a)
5/6x:3/2=25/100
5x/6*2/3=1/4
10x/18=1/4
40x=18
x=18/40
x=9/20

b)
11/15*1/x=22/5
11/15x=22/5
330x=55
x=1/6

c)
11/4*1/x=33/8
11/4x=33/8
132x=88
x=88/132
x=2/3

d)
21/4*1/2x=49/8
21/8x=49/8
392x=168
x=168/392
x=21/49

2. a) 2x+2/5=7/4 =40x+8=35  x=27/40
    b) x/4+6/28=5/7  7x=14  x=2
    c) 5x/10+10/9=75/100 =450x/900+1000=675/900 = 450x/900=325/900
450x*900= 900*325  x=39/54
    d) 3x/5-1/2=6 =6x-5=60  6x=60-5  x=55/6  
    e)  2/9*(3x-75/100=1/3 =600x/900-150/900=1/3 =600x/900=150/900+300/900   600x/900=450/900  600x/900=1/2 x=900/1200  x=3/4
 Dupa modelul acesta le rezolvi si tu pe celelalte.
Mlta bafta