Question

$x - \frac{x - 2}{2} = 3 - \frac{x - 3}{5}$

Answer 1

$\: \: x - \frac{x - 2}{2} = 3 - \frac{x - 3}{5} \\ \\ \frac{2x - x + 2}{2} = \frac{15 - x + 3}{5} \\ \\ \: \: \: \: \: \: \: \: \: \: \frac{x + 2}{2} = \frac{18 - x}{5} \\ \\ \: \: \: \: \: 5(x +2) = 2(18 - x) \\ \: \: \: \: \: \: 5x +10 = 36 - 2x \\ \: \: \: \: \: 5x + 2x = 36 -10 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 7x = 26 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x = \frac{26}{7}$

Answer 2

$x - \frac{x - 2}{2} = 3 - \frac{x - 3}{5}$

$\frac{2x - x + 2}{2} = \frac{15 - x - 3}{5}$

$\frac{x + 2}{2} = \frac{12 - x}{5}$

${5x + 10} = {24 - 2x}$

${5x + 2x} = {24 - 10}$

${7x} = {14}$

${x} = \frac{14}{7}$

${x} = {2}$