a)
[tex] \frac{x - 3}{4} - \frac{3}{2} + \frac{2x}{5} = 1 \\ 5x - 15 - 30 + 8x - 4 = 20 \\ 13x - 49 = 20 \\ 13x = 69 \\ x = \frac{69}{13} [/tex]
b)
[tex] \frac{12x - 5}{4} + \frac{2 - x}{3} = 3 - 2x \\ 36x - 15 + 8 - 4x = 36 - 24x \\ 32x - 7 = 36 - 24x \\ 56x = 43 \\ x = \frac{43}{56} [/tex]
c)
[tex] \frac{x - 3}{2} - \frac{x}{5} + \frac{3}{4} = \frac{2x - 4}{10} \\ 10x - 30 - 4x + 15 = 4x - 6 \\ 6x - 15 = 4x - 6 \\ 2x = 9 \\ x = \frac{9}{2} [/tex]
d)
[tex] \frac{x + 4}{2} - \frac{2x + 3}{4} + \frac{5}{3} = 2 \times \frac{1}{2} + \frac{5x + 3}{6} \\ \frac{x + 4}{2} - \frac{2x + 3}{4} + \frac{5}{3} = \frac{5}{2} + \frac{5x + 3}{6} \\ 6x + 24 - 6x - 9 + 20 = 30 + 10x + 6 \\ 35 = 36 + 10x \\ - 10x = 1 \\ x = - \frac{1}{10} [/tex]
e)
[tex] \frac{2 - 3x}{3} + \frac{2 + 5x}{4} = 2x - 3 \\ 8 - 12x + 6 + 15x = 24x - 36 \\ 14 + 3x = 24 - 36 \\ 3x - 24x = - 14 -36 \\ - 21x = - 56 \\ x = \frac{50}{21} [/tex]
f)
[tex] \frac{7x - 3}{2} + \frac{2 - 5x}{24} = \frac{5x + 1}{6} - \frac{3x + 2}{4} \\ 84x - 36 + 2 - 5x = 20x + 4 - 18x - 12 \\ 79x - 34 = 2x - 8 \\ 79x - 2x = - 8 + 34 \\ 77x = 26 \\ x = \frac{26}{77} [/tex]
