a)
[tex] \frac{2x + 1}{x - 3} = 4[/tex]
[tex]2x + 1 = 4 (x - 3)[/tex]
[tex]2x + 1 = 4x - 12[/tex]
[tex] - 2x = - 12 - 1[/tex]
[tex] - 2x = - 13[/tex]
[tex]x = \frac{ - 13}{ - 2} = 6 \frac{1}{2} [/tex]
b)
[tex] \frac{x + 4}{x - 1} = 4[/tex]
[tex]4(x - 1) = x + 4[/tex]
[tex]4x - 4 = x + 4[/tex]
[tex]3x = 8[/tex]
[tex]x = \frac{8}{3} = 2 \frac{2}{3} [/tex]
c)
[tex] \frac{x}{x + 1 } = 8[/tex]
[tex]8(x + 1) = x[/tex]
[tex]8x + 8 = x[/tex]
[tex]7x = - 8[/tex]
[tex]x = \frac{ - 8}{7} = - 1 \frac{1}{7} [/tex]
d)
[tex] \frac{7 - x}{x + 2} = \frac{1}{3} [/tex]
[tex]3(7 - x) = x + 2[/tex]
[tex]21 - 3x = x + 2[/tex]
[tex] - 3x - x = 2 - 21[/tex]
[tex] - 4x = - 19[/tex]
[tex]x = \frac{ - 19}{ - 4} = 4 \frac{3}{4} [/tex]
e)
[tex] \frac{3x + 2}{3x - 2} = 3[/tex]
[tex]3(3x - 2) = 3x + 2[/tex]
[tex]9x - 6 = 3x + 2[/tex]
[tex]6x = 8[/tex]
[tex]x = \frac{8}{6} = \frac{4}{3} = 1 \frac{1}{3} [/tex]
f)
[tex] \frac{4x + 5}{5x - 1} = 1[/tex]
[tex]4x + 5 = 5x - 1[/tex]
[tex] - x = - 6[/tex]
[tex]x = 6[/tex]
