19.
a)
[tex]\frac{3-x}{2}+\frac{x+2}{2} = \frac{1}{2} \ \ /\cdot 2\\\\3-x+x+2 = 1\\\\-x+x = 1-5\\\\0=-4, \ sprzecznosc, \ brak \ rozwiazania\\\\0 \neq -4[/tex]
b)
[tex]\frac{1}{4}x -\frac{x-1}{4}=\frac{1}{4} \ \ /\cdot 4\\\\x-(x-1) = 1\\\\x-x+1 = 1\\\\x-x = 1-1\\\\0 = 0[/tex]
Równanie tożsamościowe, nieskończenie wiele rozwiązań.
c)
[tex]\frac{x+1}{2}+\frac{2x-2}{3} = \frac{2x-6}{6} \ \ /\cdot6\\\\3(x+1) + 2(2x-2) = 2x-6\\\\3x+3 +4x-4 = 2x-6\\\\7x-1 = 2x-6\\\\7x-2x = -6+1\\\\5x = -5 \ \ /:5\\\\\underline{x = -1}[/tex]
d)
[tex]\frac{2x+3}{3}+\frac{x-4}{5} = \frac{3x+5}{10} \ \ /\cdot30\\\\10(2x+3) + 6(x-4) = 3(3x+5)\\\\20x+30+6x-24 = 9x+15\\\\26x+6 = 9x + 15\\\\26x-9x = 15 - 6\\\\17x = 9 \ \ /:17\\\\\underline{x = \frac{9}{17}}[/tex]
