Odpowiedź:
zad 4
a)
(5x - 3)/4 + 3 = 2x | * 4
5x - 3 + 12 = 8x
5x + 9 = 8x
5x - 8x = - 9
- 3x = - 9
3x = 9
x = 9/3 = 3
b)
x - (2x + 3)/5 = 3 | * 5
5x - 2x - 3 = 15
3x = 15 + 3 = 18
x = 18/3 = 6
c)
4 - x/4 = 2x - 1/2 | * 4
16 - x = 8x - 2
- x - 8x = - 2 - 16
- 9x = - 18
9x = 18
x = 18/9 = 2
d)
2x/3 + 4 = (x + 2)/3 | * 3
2x + 12 = x + 2
2x - x = 2 - 12
x = - 10
zad 5
a)
(x - 5)/2 = x/3
3(x - 5) = 2x
3x - 5 = 2x
3x - 2x = 5
x = 5
b)
(4x - 1)/2 = (5x + 3)/3
3(4x - 1) = 2(5x + 3)
12x - 3 = 10x + 6
12x - 10x = 6 + 3
2x = 9
x = 9/2 = 4 1/2 = 4,5
zad 6
a)
3(2x - 5) = 2(3x - 5)
6x - 15 = 6x - 10
6x - 6x = - 10 + 15
0 ≠ 5 równanie sprzeczne x ∈ ∅ (zbiór pusty)
c)
x/3 + x = 2 * 2x/3
(x + 3x)/3 = 4x/3
3(x +3x) = 3 * 4x
3 * 4x = 12x
12x = 12x
12x - 12x = 0
0 = 0 równanie tożsamościowe , spełnia je każda liczba ze zbioru liczb rzeczywistych
x ∈ R
