Question

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Answer 1

$\frac{x}{2} + \frac{x}{3} = 1 \\ \\ \frac{3x}{6} + \frac{2x}{6} = 1 \\ \\ \frac{3x + 2x}{6} = 1 \\ \\ 5x = 6 \\ \\ x = \frac{6}{5} = 1.2$

$\frac{x + 1}{3} + \frac{x + 2}{4} = 6 \\ \\ \frac{4(x + 1)}{12} + \frac{3(x + 2)}{12} = 6 \\ \\ \frac{4x + 4}{12} + \frac{3x + 6}{12} = 6 \\ \\ \frac{4x + 4 + 3x + 6}{12} = 6 \\ \\ \frac{7x + 10}{12} = 6 \\ \\ 7x + 10 = 72 \\ \\ 7x = 62 \\ \\ x = \frac{62}{7} = 8 \frac{6}{7}$

$\frac{2x - 7}{4} - \frac{4x - 3}{3} = \frac{x}{6} + \frac{5}{4} \\ \\ \frac{3(2x - 7)}{12} - \frac{4(4x - 3)}{12} = \frac{2x}{12} + \frac{15}{12} \\ \\ \frac{6x - 21}{12} - \frac{16x - 12}{12} = \frac{2x + 15}{12} \\ \\ \frac{6x - 21 - 16x + 12}{12} = \frac{2x + 15}{12} \\ \\ \frac{ - 10x - 9}{12} = \frac{2x + 15}{12} \\ \\ - 10x - 9 = 2x + 15 \\ \\ 10x + 2x = - 9 - 15 \\ \\ 12x = - 24 \\ \\ x = - 2$

$\frac{x - 5}{3} + \frac{2x - 1}{5} = \frac{6x - 23}{15} \\ \\ \frac{5(x - 5)}{15} + \frac{3(2x - 1)}{15} = \frac{6x - 23}{15} \\ \\ \frac{5x - 25}{15} + \frac{6x - 3}{15} = \frac{6x - 23}{15} \\ \\ \frac{5x - 25 + 6x - 3}{15} = \frac{6x - 23}{15} \\ \\ \frac{11x - 28}{15} = \frac{6x - 23}{15} \\ \\ 11x - 28 = 6x - 23 \\ \\ 11x - 6x = 28 - 23 \\ \\ 5x = 5 \\ \\ x = 1$