a) 3(x + 3) = 2(x + 4) + x + 1
3x + 9 = 2x + 8 + x + 1
3x - 2x - x = 8 + 1 - 9
0 = 0
b) 2x - 4-3(2 - x) = 5(2x - 1)
2x - 4 - 6 + 3x = 10x - 5
2x + 3x - 10x = 6 + 4 - 5
-5x = 5
x = -1
c) 5(x + 4) - (2x - 3) = 2(1 - 2x)
5x + 20 - 2x + 3 = 2 - 4x
5x - 2x + 4x = 2 - 3 - 20
7x = -21
x = -3
d) 4(x - 2) - 2(x-4) = 5(x + 1) - 3x
4x - 8 - 2x + 8 = 5x + 5 - 3x
4x - 2x - 5x + 3x = 5 + 8 - 8
0 = 5
Odpowiedź:
[tex]a)\\\\3(x+3)=2(x+4)+x+1\\\\3x+9=2x+8+x+1\\\\3x+9=3x+9\\\\3x-3x=9-9\\\\0=0\\\\R\'ownanie\ \ to\.zsamo\'sciowe\ \ ma\ \ niesko\'nczenie\ \ wiele\ \ rozwiaza\'n\\\\\\b)\\\\2x-4-3(2-x)=5(2x-1)\\\\2x-4-6+3x=10x-5\\\\5x-10=10x-5\\\\5x-10x=-5+10\\\\-5x=5\ \ /:(-5)\\\\x=-1[/tex]
[tex]c)\\\\5(x+4)-(2x-3)=2(1-2x)\\\\5x+20-2x+3=2-4x\\\\3x+23=2-4x\\\\3x+4x=2-23\\\\7x=-21\ \ /:7\\\\x=-3\\\\\\d)\\\\4(x-2)-2(x-4)=5(x+1)-3x\\\\4x-8-2x+8=5x+5-3x\\\\2x=2x+5\\\\2x-2x=5\\\\0=5\\\\R\'ownanie\ \ sprzeczne\ \ nie\ \ ma\ \ rozwiazania[/tex]
[tex]e)\\\\6x-(4x+5)=2(x-2)-1\\\\6x-4x-5=2x-4-1\\\\2x-5=2x-5\\\\2x-2x=-5+5\\\\0=0\\\\R\'ownanie\ \ to\.zsamo\'sciowe\ \ ma\ \ niesko\'nczenie\ \ wiele\ \ rozwiaza\'n\\\\\\f)\\\\4(3x+2)+5(2x+3)=-(2x+13)\\\\12x+8+10x+15=-2x-13\\\\22x+23=-2x-13\\\\22x+2x=-13-23\\\\24x=-36\ \ /:24\\\\x=-\frac{36}{24}\\\\x=-\frac{3}{2}\\\\x=-1\frac{1}{2}[/tex]