1) 3x - 4 = 2x - 2
3x - 2x = -2 + 4
x = 2
Sprawdzenie:
3*2 - 4 = 2*2 - 2
6 - 4 = 4 - 2
2 = 2
2) 3(x-1) = x-4
3x - 3 = x - 4
3x - x = -4 + 3
2x = -1
x = [tex]-\frac{1}{2}[/tex]
Sprawdzenie:
[tex]3(-\frac{1}{2} - 1) = -\frac{1}{2} - 4[/tex]
[tex]3*(-\frac{3}{2}) = -\frac{9}{2}[/tex]
[tex]-\frac{9}{2} = -\frac{9}{2}[/tex]
3) 2x - (1-x) = 11 - x
2x - 1 + x = 11 - x
3x - 1 = 11 - x
3x + x = 11 + 1
4x = 12
x = 3
Sprawdzenie:
2*3 - (1-3) = 11 - 3
6 - (-2) = 8
6 + 2 = 8
8 = 8
4) [tex]2x - \frac{1}{2}(3x -2) = \frac{7}{4} - x[/tex]
[tex]2x - \frac{3}{2}x + 1 = \frac{7}{4} - x[/tex] /*4
[tex]8x - 6x + 4 = 7 - 4x[/tex]
[tex]2x + 4 = 7 - 4x[/tex]
[tex]2x + 4x = 7 - 4[/tex]
[tex]6x = 3[/tex]
[tex]x = \frac{3}{6} = \frac{1}{2}[/tex]
Sprawdzenie:
[tex]2*\frac{1}{2} - \frac{1}{2}(3*\frac{1}{2} - 2) = \frac{7 }{4} -\frac{1}{2}[/tex]
[tex]1 - \frac{1}{2}(\frac{3}{2} - 2) = \frac{5}{4}[/tex]
[tex]1 - \frac{1}{2}(-\frac{1}{2}) = \frac{5}{4}[/tex]
[tex]1 + \frac{1}{4} = \frac{5}{4}[/tex]
[tex]\frac{5}{4} = \frac{5}{4}[/tex]
5) [tex]\frac{2-x}{6} - \frac{x-4}{2} = \frac{3x+5}{3}[/tex] /*6
[tex]2 - x - 3(x-4) = 2(3x+5)[/tex]
[tex]2 - x - 3x + 12 = 6x + 10[/tex]
[tex]14 - 4x = 6x + 10[/tex]
[tex]-4x - 6x = 10 - 14[/tex]
[tex]-10x = -4[/tex]
[tex]x = \frac{4}{10}[/tex]
[tex]x = \frac{2}{5}[/tex]
Sprawdzenie:
[tex]\frac{2-\frac{2}{5} }{6} - \frac{\frac{2}{5} - 4 }{2} = \frac{3*\frac{2}{5} +5 }{3}[/tex]
[tex]\frac{\frac{8}{5} }{6} - \frac{\frac{18}{5} }{2} = \frac{5\frac{6}{5} }{3}[/tex]
[tex]\frac{8}{5} * \frac{1}{6} - (-\frac{18}{5}) * \frac{1}{2} = \frac{31}{5} * \frac{1}{3}[/tex]
[tex]\frac{4}{15} + \frac{9}{5} = \frac{31}{15}[/tex]
[tex]\frac{4}{15} + \frac{27}{15} = \frac{31}{15}[/tex]
[tex]\frac{31}{15} = \frac{31}{15}[/tex]
