[tex]a) \\ \\ \frac{1}{3}x - 5 = \frac{1}{2}(x - 1) - 3 \\ \\ \frac{x}{3} - 5 = \frac{1 - x}{2} - 3 \\ \\ 2x - 30 = 3(1 - x) - 18 \\ \\ 2x - 30 = 3 - 3x - 18 \\ \\ 2x - 30 = - 3x - 15 \\ \\ 2x = - 3x - 15 + 30 \\ \\ 2x = - 3x + 15 \\ \\ 2x + 3x = 15 \\ \\ 5x = 15 \\ \\ x = \frac{15}{5} = 3 \\ \\ b) \\ \\ 3x - 1 + 1 \frac{1}{2} = x + \frac{1}{2} \\ \\ 3x + 1 \frac{1}{2} = x + \frac{1}{2} + 1 \\ \\ 3x + \frac{1 \times 2 + 1}{2} = x + \frac{1}{2} + 1 \\ \\ 3x + \frac{2 + 1}{2} = x + \frac{1}{2} + 1 \\ \\ 3x + \frac{3}{2} = x + \frac{1}{2} + 1 \\ \\ 3x + \frac{3}{2} = x + \frac{3}{2} \\ \\ 3x = x \\ \\ 3x - x = 0 \\ \\ 2x = 0 \\ \\ x = 0 \\ \\ c) \\ \\ \frac{3}{5}(x - 2) + x = 1 \frac{1}{5}(x + 1) \\ \\ \frac{3}{5}(x - 2) + x = \frac{1 \times 5 + 1}{5}(x + 1) \\ \\ \frac{3}{5}(x - 2) + x = \frac{5 + 1}{5}(x + 1) \\ \\ \frac{3}{5}(x - 2) + x = \frac{6}{5}(x + 1) \\ \\ \frac{3x}{5} - 2 + x = \frac{6x}{5} + 1 \\ \\ \frac{8x}{5} - 2 = \frac{6x}{5} + 1 \\ \\ 8x - 10 = 6x + 5 \\ \\ 8x = 6x + 5 + 10 \\ \\ 8x = 6x + 15 \\ \\ 8x - 6x = 15 \\ \\ 2x = 15 \\ \\ x = \frac{15}{2} \\ \\ d) \\ \\ \frac{2}{7}(x + 3) + \frac{x}{2} = \frac{12}{14}(x - 4) \\ \\ \frac{2(x + 3)}{7} + \frac{x}{2} = \frac{6}{7}(x - 4) \\ \\ \frac{2(x + 3)}{7} + \frac{x}{2} = \frac{6(x - 4)}{7} \\ \\ 4(x + 3) + 7x = 12(x - 4) \\ \\ 4x + 12x + 7x = 12x - 48 \\ \\ 11x + 12 = 12x - 48 \\ \\ 12 = 12x - 48 - 11x \\ \\ 12 = x - 48 \\ \\ 12 + 48 = x \\ \\ 60 = x \\ \\ x = 60 \\ \\ e) \\ \\ 1 \frac{2}{5}(x + 3) - 2 \frac{1}{3} = \frac{4}{5}(x - 1) - x \\ \\ \frac{1 \times 5 + 2}{5}(x + 3) - 2 \frac{1}{3} = \frac{4}{5}(x - 1) - x \\ \\ \frac{5 + 2}{5}(x + 3) - 2 \frac{1}{3} = \frac{4}{5}(x - 1) - x \\ \\ \frac{7}{5}(x + 3) - 2 \frac{1}{3} = \frac{4}{5}(x - 1) - x \\ \\ \frac{7}{5}(x + 3) - \frac{2 \times 3 + 1}{3} = \frac{4}{5}(x - 1) - x \\ \\ \frac{7}{5}(x + 3) - \frac{6 + 1}{4} = \frac{4}{5}(x - 1) - x \\ \\ \frac{7}{5}(x + 3) - \frac{7}{3} = \frac{4}{5}(x - 1) - x \\ \\ \frac{7x}{5} + 3 - \frac{7}{3} = \frac{4x}{5} - 1 - x \\ \\ \frac{7x}{5} + \frac{2}{3} = - \frac{x}{5} - 1 \\ \\ 7x + \frac{10}{3} = - x - 5 \\ \\ 7x + \frac{10}{3} + x = - 5 \\ \\ 8x + \frac{10}{3} = - 5 \\ \\ 8x = - 5 - \frac{10}{3} = - \frac{25}{3} \\ \\ x = - \frac{25}{3 \times 8} = - \frac{25}{24} \\ \\ f) \\ \\ \frac{x - 3}{4} - \frac{2}{3}x = \frac{5}{6}(x + 1) + \frac{1}{2} \\ \\ \frac{x - 3}{4} - \frac{2x}{3} = \frac{5}{6}(x + 1) + \frac{1}{2} \\ \\ \frac{x - 3}{4} - \frac{2x}{3} = \frac{5(x + 1)}{6} + \frac{1}{2} \\ \\ 3(x - 3) - 8x = 10(x + 1) + 6 \\ \\ 3x - 9 - 8x = 10x + 10 + 6 \\ \\ - 5x - 9 = 10x + 10 + 6 \\ \\ - 5x - 9 = 10x + 16 \\ \\ - 9 = 10x + 16 + 5x \\ \\ - 9 = 15x + 16 \\ \\ - 9 - 16 = 15x \\ \\ - 25 = 15x \\ \\ - \frac{25}{15} = x \\ \\ - \frac{5}{3} = x \\ \\ x = - \frac{5}{3} [/tex]
