Odpowiedź:
a) [tex]\frac{x}{2}[/tex] - [tex]\frac{2x+1}{3}[/tex] = 0 |×6
3x - 2(2x + 1) = 0
3x - 4x - 2 = 0
-x = 2
x = -2
b) [tex]\frac{5x}{3}[/tex] - [tex]\frac{x-2}{4}[/tex] = 1 |×12
20x - 3(x - 2) = 12
20x - 3x + 6 = 12
17x = 6
x = [tex]\frac{6}{17}[/tex]
c) 2x - [tex]\frac{x-3}{5}[/tex] = 6 |×5
10x - (x - 3) = 30
10x - x + 3 = 30
9x = 27
x = 3
d) [tex]\frac{x-3}{5}[/tex] - [tex]\frac{2x}{3}[/tex] = 3 - x |×15
3(x - 3) - 10x = 15(3 - x)
3x - 9 - 10x = 45 - 15x
3x - 10x + 15x = 45 + 9
8x = 54
x = 6[tex]\frac{3}{4}[/tex]
e) 2x - [tex]\frac{4x}{3}[/tex] = [tex]\frac{x+2}{2}[/tex] |×6
12x - 8x = 3(x + 2)
4x = 3x + 6
x = 6
f) [tex]\frac{x-2}{3}[/tex] - ([tex]\frac{-3x}{4}[/tex]) = 1
[tex]\frac{x-2}{3}[/tex] + [tex]\frac{3x}{4}[/tex]) = 1 |×12
4(x - 2) + 9x = 12
4x - 8 + 9x = 12
13x = 20
x = [tex]\frac{20}{13}[/tex] = 1[tex]\frac{7}{13}[/tex]
g) 5x - [tex]\frac{3x-2}{3}[/tex] = x - 2 |×3
15x - (3x - 2) = 3(x - 2)
15x - 3x + 2 = 3x - 6
12x - 3x = -6 - 2
9x = -8
x = -[tex]\frac{8}{9}[/tex]
h) 4x - 3 = [tex]\frac{5x}{3}[/tex] - [tex]\frac{3+x}{5}[/tex] |×15
60x - 45 = 25x - 3(3 + x)
60x - 45 = 25x - 9 - 3x
60x - 25x + 3x = -9 + 45
38x = 36
x = [tex]\frac{36}{38}[/tex] = [tex]\frac{18}{19}[/tex]
i) 2 - [tex]\frac{4x-5}{4}[/tex] = [tex]\frac{x}{2}[/tex] - 3 |×4
8 - (4x - 5) = 4([tex]\frac{x}{2}[/tex] - 3)
8 - 4x + 5 = 2x - 12
-4x - 2x = -12 - 5 - 8
-6x = -25
x = [tex]\frac{25}{6}[/tex] = 4[tex]\frac{1}{6}[/tex]
j) 5x - [tex]\frac{3x+1}{2}[/tex] = [tex]\frac{3x}{8}[/tex] + 1 |×8
40x - 4(3x + 1) = 8([tex]\frac{3x}{8}[/tex] + 1)
40x - 12x - 4 = 3x + 8
28x - 3x = 8 + 4
25x = 12
x = [tex]\frac{12}{25}[/tex]
k) [tex]\frac{x-3}{2}[/tex] - [tex]\frac{x+1}{3}[/tex] = 2 |×6
3(x - 3) - 2(x + 1) = 12
3x - 9 - 2x - 2 = 12
x = 12 + 2 + 9
x = 23
l) [tex]\frac{2x-5}{4}[/tex] - [tex]\frac{x-3}{3}[/tex] = x + 2 |×12
3(2x - 5) - 4(x - 3) = 12(x + 2)
6x - 15 - 4x + 12 = 12x + 24
2x - 12x = 24 - 12 + 15
-10x = 27
x = -[tex]\frac{27}{10}[/tex] = -2[tex]\frac{7}{10}[/tex]
