Rozwiąż równania proszę o pomoc zdjęcie w załączniku

[tex]a)\\\\2-5(3x-4)=5(6+x)\\\\2-15x+20=30+5x\\\\22-15x=30+5x\\\\-15x-5x=30-22\\\\-20x=8\ \ /:(-20)\\\\x=-\frac{8}{20}\\\\x=-\frac{2}{5}\\\\\\b)\\\\x+\frac{x}{2}-1=2x-\frac{x}{2}+1\ \ /\cdot2\\\\2x+x-2=4x-x+2\\\\3x-2=3x+2\\\\3x-3x=2+2\\\\0=4\\\\R\'ownanie\ \ sprzeczne\ \ nie\ \ ma\ \ rozwiazania[/tex]

[tex]c)\\\\\frac{2x-3}{5}=\frac{x}{3}\\\\3(2x-3)=5x\\\\6x-9=5x\\\\6x-5x=9\\\\x=9\\\\\\d)\\\\(x+2)(x-1)=x(x+5)\\\\x^2-x+2x-2=x^2+5x\\\\x^2+x-x^2-5x=2\\\\-4x=2\ \ /:(-4)\\\\x=-\frac{2}{4}\\\\x=-\frac{1}{2}\\\\\\e)\\\\\frac{1}{x}=\frac{5}{2x+1}\\\\x\neq 0\ \ i\ \ 2x+1\neq 0\\\\x\neq 0\ \ i\ \ 2x\neq -1\ \ /:2\\\\x\neq 0\ \ i\ \ x\neq -\frac{1}{2}\\\\D=R\setminus\left\{-\frac{1}{2},0\right\}\\\\\frac{1}{x}=\frac{5}{2x+1}\\\\2x+1=5x\\\\2x-5x=-1[/tex]

[tex]-3x=-1\ \ /:(-3)\\\\x=\frac{1}{3}\\\\\\f)\\\\\frac{-x}{2x-4}=\frac{3x}{1-6x}\\\\2x-4\neq 0\ \ i\ \ 1-6x\neq 0\\\\2x\neq 4\ \ /:2\ \ i\ \ -6x\neq -1\ \ /:(-6)\\\\x\neq 2\ \ i\ \ x\neq \frac{1}{6}\\\\D=R\setminus\left\{2,\frac{1}{6}\right\}\\\\\\\frac{-x}{2x-4}=\frac{3x}{1-6x}\\\\-x(1-6x)=3x(2x-4)\\\\-x+6x^2=6x^2-12x\\\\-x+6x^2-6x^2+12x=0\\\\11x=0\ \ /:11\\\\x=0[/tex]

Krysiaviz Krysiaviz · Answer 2

[tex]a)\\\\2-5(3x-4)=5(6+x)\\\\2-15x+20=30+5x\\\\-15x-5x=30-20-2\\\\-20x=8\ \ |:(-20)\\\\x=-\frac{8}{20}=\frac{2}{5}[/tex]

[tex]b)\\\\ x+ \frac{x}{2}-1=2x- \frac{x}{2}+1 \\\\x+\frac{x}{2}+\frac{x}{2}-2x=1+1\\\\2x-2x=2\\\\0=2\\\\rownanie\ sprzeczne, brak\ rozwiazania[/tex]

[tex]c)\\\\ \frac{2x-3}{5}=\frac{x}{3}\ \ |*15\\\\3(2x-3)=5x\\\\6x-9=5x\\\\6x-5x=9\\\\ x=9[/tex]

[tex]d)\\\\ (x+2)(x-1)=x(x+5)\\\\x^2-x+2x-2=x^2+5x\\\\x^2+x-x^2-5x=2\\\\-4x=2\ \ |:(-4)\\\\x=-\frac{2}{4}=-\frac{1}{2}[/tex]

[tex]e)\\\\ \frac{1}{x}=\frac{5 }{2x+1} \\\\ 2x+1=0\ \ i\ \ x\neq 0\\\\2x=-1\ \ |:2\\\\x\neq -\frac{1}{2}\\\\D=R\setminus \left\{ -\frac{1}{2},0\right\}\\\\ 5x=2x+1\\\\5x-2x=1\\\\3x=1\ \ |:3\\\\x=\frac{1}{3}[/tex]

[tex]f)\\\\ \frac{-x}{2x-4}=\frac{3x}{1-6x}\\\\2x-4\neq 0\ \ i\ \ 1-6x\neq 0\\\\ 2x \neq 4\ \ |:2\ \ i\ \ -6x\neq -1\ \ |:(-6)\\\\x\neq 2\ \ i\ \ x\neq \frac{1}{6}\\\\D=R\setminus \left\{ \frac{1}{6},2\right\}\\\\ -x(1-6x)=3x(2x-4)\\\\-x+6x^2=6x^2-12x\\\\ -x+6x^2-6x^2+12x=0\\\\11x=0\ \ |:11\\\\x=0[/tex]