Odpowiedź:
a)
(4x + 7)/2 = x + 5 + (5x - 1)/6
2x + 7/2 = x + 5 + 5/6x - 1/6
2x - 1 5/6x = 4 5/6 - 7/2
1/6x = 4 5/6 - 3 1/2 /*6
x = 6(4 5/6 - 3 3/6) = 6 * 1 2/6 = 6 * 8/6 = 8
c)
(x + 5)/4 = 1/2(2 - x) + (2x + 1)/8 /*8
2(x + 5) = 4(2 - x) + 2x + 1
2x + 10 = 8 - 4x + 2x + 1
2x + 2x = 9 - 10
4x = -1 /:4
x = -1/4
e)
4x/9 - 5x/12 = 1
4/9x - 5/12x = 1
16/36x - 15/36x = 1
1/36x = 1 /*36
x = 36
g)
(2x - 7)/3 = (3x + 2)/4
2/3x - 7/3 = 3/4x + 1/2
2/3x - 3/4x = 1/2 + 7/3
8/12x - 9/12x = 3/6 + 2 1/3
-1/12x = 3/6 + 2 2/6 /*(-12)
x = -12 * 2 5/6 = -12 * 17/6 = -34
i)
(5 - z)/8 = (18 - 5z)/12
5/8 - 1/8z = 18/12 - 5/12z
-1/8z + 5/12z = 1 6/12 - 5/8
-3/24z + 10/24z = 1 1/2 - 5/8
7/24z = 1 4/8 - 5/8 /*24/7
z = 24/7(12/8 - 5/8) = 24/7 * 7/8 = 3
k)
(4t + 33)/21 = (17 + t)/14
4/21t + 33/21 = 17/14 + 1/14t
4/21t - 1/14t = 1 3/14 - 1 12/21
3/21t = 1 9/42 - 1 24/42
1/7t = -15/42 /*7
t = -15/6 = -2 3/6 = -2 1/2
m)
(1 - 9y)/5 = (19 + 3y)/8
1/5 - 9/5y = 19/8 + 3/8y
-1 4/5y - 3/8y = 2 3/8 - 1/5
-1 32/40y - 15/40y = 2 15/40 - 8/40
-1 47/40y = 2 7/40
-87/40y = 87/40 /*(-40/87)
y = -1
o)
(3x - 12)/2 + x = 5 - 2x
3/2x - 6 + x = 5 - 2x
2 1/2x + 2x = 5 + 6
4 1/2x = 11
9/2x = 11 /*2/9
x = 11 * 2/9 = 22/9 = 2 4/9
q)
x = 1/5(1 - x/2) + 2(x - 1)
x = 1/5 - 1/10x + 2x - 2
x - 1 9/10x = -1 4/5
-9/10x = -9/5 /*(-10/9)
x = 2
s)
(5x - 2)/2 - (3x - 1)/3 = 1
5/2x - 1 - x + 1/3 = 1
2 1/2x - x = 1 + 2/3
1 1/2x = 1 2/3
3/2x = 5/3 /*2/3
x = 5/3 * 2/3 = 10/9 = 1 1/9
Szczegółowe wyjaśnienie:
