Odpowiedź:
a)
(x + 3)/(x -1) = 2/3
założenie:
x - 1 ≠ 0
x ≠ 1
D: x ∈ R\{1}
(x + 3)/(x - 1) = 2/3
3(x + 3) = 2(x -1)
3x + 9 = 2x - 2
3x - 2x = - 2 - 9
x = - 11
b)
3(x - 1)/5 - (x - 3)/2 = (x -8)/10 | * 10
2 * 3(x - 1) - 5(x - 3) = x - 8
6x - 6 - 5x + 15 = x - 8
x - 6 = x - 8
x -x = - 8 + 6
0 ≠ - 2
równanie sprzeczne x ∈ ∅(zbiór pusty)
c)
2 - √2x = x - 4
- √2x - x = - 4 - 2
- x(√2 - 1) = - 6
x(√2 - 1) = 6
x = 6/(√2 - 1) = 6(√2 + 1)/[(√2 - 1)(√2 +1)] = 6(√2 + 1)/(2 - 1) = 6(√2 + 1)
d)
2(x - 1) - 3(x - 2) < 6
2x - 2 - 3x + 6 < 6
- x + 4 < 6
- x < 6 - 4
- x < 2
x > - 2
x ∈ ( - 2 , + ∞ )
e)
- 2x + 4 ≥ 6 - x√2
- 2x + x√2 ≥ 6 - 4
x( √2 - 2) ≥ 2
x ≥ 2/(√2 - 2)
x ≥ 2(√2 + 2)/[(√2 - 2)(√2 +2)]
x ≥ 2(√2 + 2)/(2 - 4)
x ≥ 2(√2 + 2)/(- 2)
x ≥ - (√2 + 2)
x ∈ < - (√2 + 2) ; + ∞ )
