[tex]a) \frac{x + 3}{2} - \frac{1}{2} + \frac{2x + 7}{10} = 1 \: | \times 10[/tex]
[tex]5(x + 3) - 5 + 2x + 7 = 10[/tex]
[tex]5x + 15 - 5 + 2x + 7 = 10[/tex]
[tex]5x + 2x = 10 - 15 + 5 - 7[/tex]
[tex]7x = - 7 \: | \div 7[/tex]
[tex]x = - 1[/tex]
[tex]b) \frac{11x - 4}{4} + \frac{1 - x}{2} = 6 - x \: | \times 4[/tex]
[tex]11x - 4 + 2(1 - x) = 24 - 4x[/tex]
[tex]11x - 4 + 2 - 2x = 24 - 4x[/tex]
[tex]11x - 2x + 4x = 24 + 4 - 2[/tex]
[tex]13x = 26 \: | \div 13[/tex]
[tex]x = 2[/tex]
[tex]c) \frac{x - 4}{6} - \frac{x}{5} + \frac{3}{2} = \frac{2x - 1}{10} \: | \times 30[/tex]
[tex]5(x - 4) - 6x + 45 = 3(2x - 1)[/tex]
[tex]5x - 20 - 6x + 45 = 6x - 3[/tex]
[tex]5x - 6x - 6x = - 3 + 20 - 45[/tex]
[tex] - 7x = - 28 \: | \div ( - 7)[/tex]
[tex]x = 4[/tex]
[tex]d) \frac{x + 2}{3} - \frac{2x + 3}{4} + \frac{5}{3} = 1 \frac{5}{6} + \frac{7x - 11}{12} [/tex]
[tex] \frac{x + 2}{3} - \frac{2x + 3}{4} + \frac{5}{3} = \frac{1 \times 6 + 5}{6} + \frac{7x - 11}{12} [/tex]
[tex] \frac{x + 2}{3} - \frac{2x + 3}{4} + \frac{5}{3} = \frac{11}{6} + \frac{7x - 11}{12} \: | \times 12[/tex]
[tex]4(x + 2) - 3(2x + 3) + 20 = 22 + 7x - 11[/tex]
[tex]4x + 8 - 6x - 9 + 20 = 22 + 7x - 11[/tex]
[tex]4x - 6x - 7x = 22 - 11 - 8 + 9 - 20[/tex]
[tex] - 9x = - 8 \: | \times ( - 1)[/tex]
[tex]9x = 8[/tex]
[tex]x = \frac{8}{9} [/tex]
[tex]e) \frac{1 - x}{3} + \frac{1 + 3x}{4} = 2x - 1 \: | \times 12[/tex]
[tex]4(1 - x) + 3(1 + 3x) = 24x - 12[/tex]
[tex]4 - 4x + 3 + 9x = 24x - 12[/tex]
[tex] - 4x + 9x - 24x = - 12 - 4 - 3[/tex]
[tex] - 19x = - 19 \: | \div ( - 19)[/tex]
[tex]x = 1[/tex]
[tex]f) \frac{7x - 12}{5} + \frac{19 - 6x}{7} = \frac{x}{2} + \frac{x - 1}{5} \: | \times 70[/tex]
[tex]14(7x - 12) + 10(19 - 6x) = 35x + 14(x - 1)[/tex]
[tex]98x - 168 + 190 - 60x = 35x + 14x - 14[/tex]
[tex]98x - 60x - 35x - 14x = - 14 + 168 - 190[/tex]
[tex] - 11x = -36 \: | \times ( - 1)[/tex]
[tex]11x = 36[/tex]
[tex]x = \frac{36}{11} [/tex]
