Odpowiedź:
zad1
a)
2x - 1 = 1 + 3x dla x = (- 2)
2 * (- 2) - 1 = 1 + 3 * (- 2)
- 4 - 1 = 1 - 6
- 5 = - 5
L = P
Liczba - 2 spełnia równanie
b)
- 2x * (1 - 2x) = - x * (2 - x) dla x = (- 1)
- 2x + 4x = - 2x + x²
- 2x + 2x + 4x - x² = 0
4x - x² = 0
4 * (- 1) - (- 1)² = 0
- 4 - 1 = 0
- 5 ≠ 0
L ≠ P
Liczba (- 1) nie spełnia równania
zad 2
a)
1 - 3x = 10
- 3x = 10 - 1
- 3x = 9
3x = - 9
x = - 9/3 = - 3
b)
5x - 1 = 7 - 3x
5x + 3x = 7 + 1
8x = 8
x = 8/8 = 1
c)
3(2x - 1) - (5 - x) = - 1
6x - 3 - 5 + x = - 1
7x - 8 = - 1
7x = - 1 + 8 = 7
x = 7/7 = 1
d)
2/5(3x - 1) = 6 | * 5
2(3x - 1) = 6 * 5 = 30
6x - 2 = 30
6x = 30 + 2 = 32
x = 32/6 = 5 2/6 = 5 1/3
e)
(5x - 1)/3 - (2 - 4x)/12 = 1 - (x - 3)/4 | * 12
4(5x - 1) - 2 + 4x = 12 - 3(x - 3)
20x - 4 - 2 + 4x = 12 - 3x + 9
24x - 6 = - 3x + 21
24x + 3x = 21 + 6
27x = 27
x = 27/27 = 1
f)
(x - 3)(4x + 7) = 4x² - 5x - 2
4x² - 12x + 7x - 21 = 4x² - 5x - 2
4x² - 4x² - 12x + 5x + 7x = - 2 + 21
0 ≠ 19
L ≠ P
x ∈ ∅ (zbiór pusty)
