Hej!
Zadanie 4 :
Podpunkt e)
[tex]\frac{x}{4}=\frac{x+3}{2}\\\\4(x+3)=2x\\\\4x+12=2x\\\\4x-2x=-12\\\\2x=-12 \ \ |:2\\\\x=-6[/tex]
Podpunkt f)
[tex]\frac{5}{x+3}=\frac{4}{x-2}\\\\x+3\neq0\longrightarrow x\neq-3\\\\x-2\neq0\longrightarrow x\neq2\\\\5(x-2)=4(x+3)\\\\5x-10=4x+12\\\\5x-4x=12+10\\\\x=22\in\mathbb{D}[/tex]
Podpunkt g)
[tex]\frac{2m-4}{3}=\frac{3m}{4}\\\\9m=4(2m-4)\\\\9m=8m-16\\\\9m-8m=-16\\\\m=-16[/tex]
Zadanie 5 :
Podpunkt d)
[tex]\frac{4x+5}{-4}=\frac{4-3x}{-2}\\\\-4(4-3x)=-2(4x+5)\\\\-16+12x=-8x-10\\\\12x+8x=-10+16\\\\20x=6 \ \ |:20\\\\x=\frac{6}{20}=\frac{3}{10}[/tex]
Podpunkt e)
[tex]\frac{3}{-2x+7}=\frac{9}{5-3x}\\\\-2x+7\neq0\longrightarrow x\neq3,5\\\\5-3x\neq0\longrightarrow x\neq\frac{5}{3}\\\\9(-2x+7)=3(5-3x)\\\\-18x+63=15-9x\\\\-18x+9x=15-63\\\\-9x=-48 \ \ |:(-9)\\\\x=\frac{48}{9}=5\frac{3}{9}=5\frac{1}{3}\in\mathbb{D}[/tex]
Podpunkt f)
[tex]\frac{2x}{4x-3}=\frac{1\frac{1}{2}x}{3x-7}\\\\\frac{2x}{4x-3}=\frac{1,5x}{3x-7}\\\\4x-3\neq0\longrightarrow x\neq\frac{3}{4}\\\\3x-7\neq0\longrightarrow x\neq\frac{7}{3}\\\\2x(3x-7)=1,5x(4x-3)\\\\6x^2-14x=6x^2-4,5x\\\\6x^2-14x-6x^2+4,5x=0\\\\-9,5x=0 \ \ |:(-9,5)\\\\x=0\in\mathbb{D}[/tex]