Odpowiedź:
a)
[tex]\frac{3x - 1}{4} - \frac{x -3}{3} = x[/tex] /*12
3(3x - 1) - 4(x - 3) = x
9x - 9 - 4x + 12 = x
3 = -4x
[tex]x = -\frac{4}{3}[/tex]
b)
-2(x + 4) + 3(2x - 1) = 2(2x + 4)
-2x - 8 +6x - 3 = 4x + 8
0x = 19 - równanie sprzeczne
c)
[tex]\frac{4x - 1}{6} = \frac{3 - 2x}{3}[/tex]
3(4x - 1) = 6(3 - 2x)
12x - 3 = 18 - 12x
24x = 21
[tex]x = \frac{21}{24} = \frac{7}{8}[/tex]
d)
(2x + 8)(7x - 2) = 0
14x² + 56x - 4x - 16 = 0
14x² + 52x - 16 = 0 | /2
7x² + 26x - 8 = 0
Δ = 676 + 224 = 900
[tex]\sqrt{\Delta} = 30[/tex]
[tex]x_{1} - \frac{-26 - 30}{2*7}\ \ \ \ \ v \ \ \ \ \ x_{2} = \frac{-26+30}{2*7}[/tex]
x₁ = - 4 v
[tex]x_{1} = - 4 \ \ \ \ \ v \ \ \ \ \ x_{2} = \frac{2}{7}[/tex]
e)
[tex]\frac{x^{2}-9}{x-3} = 0[/tex]
x² - 9 = x - 3
x² - 9 - x + 3 = 0
x² - x - 6 = 0
Δ = 1 + 24 = 25
[tex]\sqrt{\Delta} = 5[/tex]
[tex]x_{1} = \frac{1-5}{2*1} \ \ \ \ \ v \ \ \ \ \ x_{2} = \frac{1+5}{2*1}[/tex]
x₁ = -2 v x₂ = 3
