[tex]|2x-3|=|x-4|+1\\\\2x-3=x-4+1\\2x-x=-3+3\\x=0\\\\|2*0-3|=|0-4|+1\\|-3|=|-4|+1\\3\neq 4+1\\\\-(2x-3)=-(x-4)+1\\-2x+3=-x+4+1\\-2x+3=-x+5\\-2x+x=5-3\\-x=2 /:(-1)\\x=-2\\\\|2*(-2)-3|=|-2-4|+1\\|-4-3|=|-6|+1\\|-7|=6+1\\\\-(2x-3)=x-4+1\\-2x+3=x-3\\-2x-x=-3-3\\-3x=-6 /:(-2)\\x=2\\\\|2*2-3|=|2-4|+1\\|1|=|-2|+1\\1\neq 2+1\\\\2x-3=-(x-4)+1\\2x-3=-x+4+1\\2x-3=-x+5\\2x+x=5+3\\3x=8 /:3\\x=\frac83\\\\[/tex]
[tex]|2*\frac83-3|=|\frac83-4|+1\\|\frac{16}3-\frac93|=|\frac83-\frac{12}3|+1\\|\frac73|=|-\frac43|+\frac33\\\frac73=\frac43+\frac33[/tex]
[tex]x=-2 \text{ lub } x=\frac83[/tex]
