Odpowiedź:
a)
4 - x = 2x + 1
-x - 2x = 1 - 4
-3x = -3 /:(-3)
x = 1
b)
-x - 6 = 2x - 3
-x - 2x = -3 + 6
-3x = 3 /:(-3)
x = -1
c)
15(x - 1) = 85 + 15x
15x - 15 = 85 + 15x
15x - 15x = 85 + 15
0 = 100
rownanie sprzeczne
nie ma rozwiazan
d)
4x - 3 = 2(2x - 1,5)
4x - 3 = 4x - 3
4x - 4x = -3 + 3
0 = 0
rownanie tozsamosciowe
rozwiazaniem sa wszystkie liczby rzeczywiste
e)
x - (2x + 5) = 8
x - 2x - 5 = 8
-x = 8 + 5 /*(-1)
x = -13
f)
1/2x + 1/2 = 1 1/2
1/2x = 1 1/2 - 1/2 /*2
x = 2
g)
x/2 - x/3 = 2
3/6x - 2/6x = 2
1/6x = 2 /*6
x = 12
h)
1/2x - x/5 + 2 = 8
5/10x - 2/10x = 8 - 2
3/10x = 6 /*10/3
x = 20
i)
(x + 1)/3 - x = 2
1/3x + 1/3 - x = 2
-2/3x = 2 - 1/3 /*(-3/2)
x = -3/2 * 1 2/3 = -3/2 * 5/3 = -5/2 = -2 2/2
j)
1 - (4x - 7)/3 = 2x
1 - 4/3x + 7/3 = 2x
-1 1/3x - 2x = -1 - 2 1/3
-3 1/3x = -3 1/3
x = 1
k)
(x - 2)(x + 1) = x(x + 4) - 7
x² + x - 2x - 2 = x² + 4x - 7
x² - x² - x - 4x = -7 + 2
-5x = -5 /:(-5)
x = 1
l)
2(x - 5) + 15 = 3(x - 4) + 10
2x - 10 + 15 = 3x - 12 + 10
2x - 3x = -2 - 5
-x = -7 /*(-1)
x = 7
m)
5(2x - 3) - 6(3x - 4) = 5x - 4
10x - 15 - 18x + 24 = 5x - 4
-8x - 5x = -4 - 9
-13x = -13
x = 1
n)
2x/3 - 3x/2 - 1 = 5/6
2/3x - 1 1/2x = 5/6 + 1
4/6x - 1 3/6x = 1 5/6
4/6x - 9/6x = 11/6
-5/6x = 11/6 /*(-6/5)
x = -6/5 * 11/6 = -11/5 = -2 1/5
Szczegółowe wyjaśnienie:
