giải hộ với mọi người

Giải thích các bước giải:

$\begin{aligned}
& \text{1) } \dfrac{5x - 2}{3} = \dfrac{5 - 3x}{2} \\
& 2(5x - 2) = 3(5 - 3x) \\
& 10x - 4 = 15 - 9x \\
& 10x + 9x = 15 + 4 \\
& 19x = 19 \\
& x = 1 \\
& \text{2) } \dfrac{10x + 3}{12} = 1 + \dfrac{6 + 8x}{9} \\
& \dfrac{3(10x + 3)}{36} = \dfrac{36}{36} + \dfrac{4(6 + 8x)}{36} \\
& 30x + 9 = 36 + 24 + 32x \\
& 30x - 32x = 60 - 9 \\
& -2x = 51 \\
& x = -\dfrac{51}{2} \\
& \text{3) } \dfrac{7x - 1}{6} + 2x = \dfrac{16 - x}{5} \\
& \dfrac{5(7x - 1)}{30} + \dfrac{60x}{30} = \dfrac{6(16 - x)}{30} \\
& 35x - 5 + 60x = 96 - 6x \\
& 95x + 6x = 96 + 5 \\
& 101x = 101 \\
& x = 1 \\
& \text{4) } \dfrac{x}{3} - \dfrac{2x + 1}{6} = \dfrac{x}{6} - x \\
& \dfrac{2x}{6} - \dfrac{2x + 1}{6} = \dfrac{x}{6} - \dfrac{6x}{6} \\
& 2x - (2x + 1) = x - 6x \\
& 2x - 2x - 1 = -5x \\
& -1 = -5x \\
& x = \dfrac{1}{5} \\
& \text{5) } \dfrac{x - 1}{3} + \dfrac{2}{5} = x \\
& \dfrac{5(x - 1)}{15} + \dfrac{6}{15} = \dfrac{15x}{15} \\
& 5x - 5 + 6 = 15x \\
& 5x + 1 = 15x \\
& 15x - 5x = 1 \\
& 10x = 1 \\
& x = \dfrac{1}{10} \\
& \text{6) } \dfrac{3 - 2x}{5} - 3x = \dfrac{x + 1}{2} \\
& \dfrac{2(3 - 2x)}{10} - \dfrac{30x}{10} = \dfrac{5(x + 1)}{10} \\
& 6 - 4x - 30x = 5x + 5 \\
& 6 - 34x = 5x + 5 \\
& -34x - 5x = 5 - 6 \\
& -39x = -1 \\
& x = \dfrac{1}{39} \\
& \text{7) } \dfrac{3x + 2}{2} - \dfrac{3x + 1}{6} = 2x + \dfrac{5}{3} \\
& \dfrac{3(3x + 2)}{6} - \dfrac{3x + 1}{6} = \dfrac{12x}{6} + \dfrac{10}{6} \\
& 3(3x + 2) - (3x + 1) = 12x + 10 \\
& 9x + 6 - 3x - 1 = 12x + 10 \\
& 6x + 5 = 12x + 10 \\
& 6x - 12x = 10 - 5 \\
& -6x = 5 \\
& x = -\dfrac{5}{6} \\
\end{aligned}$