Odpowiedź:
a)
a)
48/x = 3/4
3x = 4 * 48 /:3
x = 192/3 = 64
b)
34/25 = 68/x
34x = 25 * 68 /:34
x = 25 * 68/34 = 25 * 2 = 50
c)
(3x - 2)/10 = 4/15
15(3x - 2) = 4 * 10
45x - 30 = 40
45x = 40 + 30 /:45
x = 70/45 = 1 25/45 = 1 5/9
d)
10/21 = (x + 1)/14 /*7
10/3 = (x + 1)/2
3(x + 1) = 2 * 10
3x + 3 = 20
3x = 20 - 3 /:3
x = 17/3 = 5 2/3
e)
6/(x - 1) = 9/16
9(x - 1) = 6 * 16
9x - 9 = 96
9x = 96 + 9 /:9
x = 105/9 = 11 2/3
f)
13/26 = 1/(2x + 1)
1/2 = 1/(2x + 1)
2x + 1 = 2
2x = 2 - 1 /:2
x = 1/2
g)
(x - 1)/(x + 1) = 2/3
3(x - 1) = 2(x + 1)
3x - 3 = 2x + 2
3x - 2x = 2 + 3
x = 5
h)
3/4 = (2x - 1)/(x + 5)
3(x + 5) = 4(2x - 1)
3x + 15 = 8x - 4
3x - 8x = -4 - 15
-5x = -19 /:(-5)
x = 19/5 = 3 4/5
i)
2/(x - 1) = 7/(2x + 1)
7(x - 1) = 2(2x + 1)
7x - 7 = 4x + 2
7x - 4x = 2 + 7
3x = 9
x = 3
j)
3/(3x - 4) = 6/(2x + 1)
3(2x + 1) = 6(3x - 4)
6x + 3 = 18x - 24
6x - 18x = -24 - 3
-12x = -27 /:(-12)
x = 27/12 = 9/4 = 2 1/4
k)
5/(2x - 1) = 10/(2x - 3) /:5
1/(2x - 1) = 2/(2x - 3)
2x - 3 = 2(2x - 1)
2x - 3 = 4x - 2
2x - 4x = -2 + 3
-2x = 1 /:(-2)
x = -1/2
l)
11/(x - 2) = 13/(x + 2)
11(x + 2) = 13(x - 2)
11x + 22 = 13x - 26
11x - 13x = -26 - 22
-2x = -48 /:(-2)
x = 24
Szczegółowe wyjaśnienie:
