Question

1.

a) 3/x = 5/7
b) 8/3,5 = 4/y
c) 5/6 = 1+t/10
d) 1/z-1 = 6,5/8
e) 2x-5/3 = 4/5
f) 10/1,5 = 8/9-3x

2.

a) 2/x = 3/x-1
b) 4/x+1 = 5/x
c) 3/5 = 2x-1/2-5x
d) 2x+1/1-2x = 2/3
e) 0,4x-1/3 = 2x-5/2
f) 4+x²/x = 2x-1/2

Answer 1

A) 3/x = 5/7
5x=21/:5
x=41/5

b) 8/3,5 = 4/y
8y=14/:8
x=17/8
d) 1/z-1 = 6,5/8
(z-1)*6,5=8
6,5z-6,5=8
6,5z=8+6,5
6,5z=14,5/:6,5
x=2 1/2
e) 2x-5/3 = 4/5
2x-25=12
2x=12+25
2x=37/:2
x=18,5

f) 10/1,5 = 8/9-3x
12=10(9-3x)
12=90-30x
30x=90-12/:30
x=23/5

2.

a) 2/x = 3/x-1
2(x-1)=3x
2x-2=3x
2x-3x=2
-x=2 /:-1
x=-2

b) 4/x+1 = 5/x
4x=5(x+1)
4x=5x+5
4x-5x=5 /:-1
x=-5
c) 3/5 = 2x-1/2-5x
5(2x-1)=3(2-5x)
10x-5=6-15x
10x+15x=6+5
25x=11/:25
x=11/25
d) 2x+1/1-2x = 2/3
(2x+1)*3=2*(1-2x)
6x+3=2-4x
10x=5/ :10
x=1/5

Answer 2

1.
a) 3/x = 5/7
x=3*7:5
x=21/5
x=4 1/5
b)8/3,5 = 4/y
y=4*3,5:8
y=14:8
y=1,75
c)5/6 = 1+t/10 /*30
25=30+3t
3t=-5
t=-1 2/3
d)1/z-1 = 6,5/8 /*8
8-8z=6,52
14,5z=8
z=5 5/7
e) 2x-5/3 = 4/5
2x-25/15=12/15 /+25:15
2x=37/15 /2
x=1 1/30
f) 10/1,5 = 8/9-3x
60/9=8/9-3x
3x=-52/9
x=1 25/27
2.
a) 2/x = 3/x-1 /*x
2=3-x
x=1
b)4/x+1=5/x
4+x=5
x=1
c) 3/5 = 2x-1/2-5x
3/5=-3x-1/2 /*10
6=-30x-5
-30x=11
x=-2 8/11
d) 2x+1/1-2x = 2/3 /*3
3=2
sprzeczne
e) 0,4x-1/3 = 2x-5/2 /*6
2,4x-=2x-15
0,4x=-13
x=-32,5
f) 4+x²/x = 2x-1/2 /*2
8+2x=4x-1
9=2x
x=4,5