Odpowiedź :
Odpowiedź:
Szczegółowe wyjaśnienie:
a) x/3 + 1 = 5/6 + x/2 /*6
2x + 6 = 5 + 3x
2x - 3x = 5 - 6
-x = - 1/:(-1)
x = 1
b) [tex]\frac{2x-3}{4} = \frac{1}{2} +x[/tex] / * 4
2x - 3 = 2 + 4x
2x- 4x = 2 + 3
-2x = 5/:(-2)
x = [tex]-\frac{5}{2}[/tex] = [tex]-2\frac{1}{2}[/tex]
c) [tex]\frac{x + 2}{9} + \frac{x - 1}{3} = 1[/tex] / * 9
x + 2 + 3(x - 1) =9
x + 2 + 3x - 3 = 9
x + 3x = 9 - 2 + 3
4x = 10/:4
x = [tex]\frac{10}{4}[/tex] = [tex]2\frac{2}{4}[/tex] = [tex]2\frac{1}{2}[/tex]
d) [tex]\frac{2x +3}{5} =\frac{2 - x}{3} +3[/tex] / *15
3(2x + 3) = 5(2 -x) + 45
6x + 9 = 10 - 5x + 45
6x + 5x = 10 + 45 - 9
11x = 46/:11
x = [tex]\frac{46}{11}[/tex] = [tex]4\frac{2}{11}[/tex]
e) [tex]\frac{3x - 5}{2} + \frac{5x - 1}{10} = 0[/tex] / *10
5(3x - 5) + 5x - 1 = 0
15x - 25 + 5x - 1 = 0
15x + 5x = 25 + 1
20x = 26/:20
x = [tex]\frac{26}{20}[/tex] = [tex]1\frac{6}{20}[/tex] = [tex]1\frac{3}{10}[/tex]
f) [tex]\frac{x}{2} -1 = \frac{2}{5}(4-x) - 4[/tex]
[tex]\frac{x}{2} -1 = \frac{8}{5} - \frac{2}{5}x - 4[/tex] / * 10
5x - 10 = 16 - 4x - 40
5x + 4x = 16 - 40 + 10
9x = -14/:9
x = [tex]-\frac{14}9}[/tex] = [tex]-1\frac{5}{9}[/tex]
h) [tex]\frac{2x - 3x + 5}{4} =\frac{-1}{4x - 1}[/tex]
[tex]\frac{- x + 5}{4} =\frac{-1}{4x - 1}[/tex]
(-x + 5)(4x - 1) = - 4
-4x² + x + 20x - 5 = - 4
-4x² + 21x - 1 = 0
Δ = 21² - 4 * (-4) * (-1) = 441 - 16 = 425
√Δ = [tex]\sqrt{425}[/tex] = 5[tex]\sqrt{17[/tex]
x₁ = [tex]\frac{-21 - 5\sqrt{17} }{2 * (-4)}[/tex] = [tex]\frac{-21 - 5\sqrt{17} }{-8}[/tex] = [tex]\frac{21 + 5\sqrt{17} }{8}[/tex]
x₂ =[tex]\frac{-21 +5\sqrt{17} }{2 * (-4)}[/tex] = [tex]\frac{-21 + 5\sqrt{17} }{-8}[/tex] = [tex]\frac{21 -5\sqrt{17} }{8}[/tex]
W podpunktach c i g zapomniałeś dodać znak "=" więc ich nie rozwiążę bo nie wiem co jest równe czemu.