Giải thích các bước giải:

$\begin{aligned}
& \text{1) } 4x - 18 = 0 \\
& 4x = 18 \\
& x = \dfrac{18}{4} \\
& x = \dfrac{9}{2} \\
& S = \left\{\dfrac{9}{2}\right\} \\
& \\
& \text{2) } 5(3 - 2x) + 3x = 5 \\
& 15 - 10x + 3x = 5 \\
& -7x = 5 - 15 \\
& -7x = -10 \\
& x = \dfrac{10}{7} \\
& S = \left\{\dfrac{10}{7}\right\} \\
& \\
& \text{3) } 10 - 5(2x - 3) = -2x + 5 \\
& 10 - 10x + 15 = -2x + 5 \\
& -10x + 25 = -2x + 5 \\
& -10x + 2x = 5 - 25 \\
& -8x = -20 \\
& x = \dfrac{5}{2} \\
& S = \left\{\dfrac{5}{2}\right\} \\
& \\
& \text{4) } (3x - 5)^2 - 2(9x^2 - 25) = 0 \\
& (3x - 5)^2 - 2(3x - 5)(3x + 5) = 0 \\
& (3x - 5)[(3x - 5) - 2(3x + 5)] = 0 \\
& (3x - 5)(3x - 5 - 6x - 10) = 0 \\
& (3x - 5)(-3x - 15) = 0 \\
& \left[\begin{array}{l} 3x - 5 = 0 \\ -3x - 15 = 0 \end{array}\right. \\
& \left[\begin{array}{l} 3x = 5 \\ -3x = 15 \end{array}\right. \\
& \left[\begin{array}{l} x = \dfrac{5}{3} \\ x = -5 \end{array}\right. \\
& S = \left\{\dfrac{5}{3}; -5\right\} \\
& \\
& \text{5) } x^2 - 25 - (x - 5)(x + 4) = 0 \\
& (x - 5)(x + 5) - (x - 5)(x + 4) = 0 \\
& (x - 5)[(x + 5) - (x + 4)] = 0 \\
& (x - 5)(x + 5 - x - 4) = 0 \\
& (x - 5) \cdot 1 = 0 \\
& x - 5 = 0 \\
& x = 5 \\
& S = \{5\} \\
& \\
& \text{6) } 10 - 3(x - 2)^2 = (x + 2)(1 - 3x) \\
& 10 - 3(x^2 - 4x + 4) = x - 3x^2 + 2 - 6x \\
& 10 - 3x^2 + 12x - 12 = -3x^2 - 5x + 2 \\
& -3x^2 + 12x - 2 = -3x^2 - 5x + 2 \\
& 12x - 2 = -5x + 2 \\
& 12x + 5x = 2 + 2 \\
& 17x = 4 \\
& x = \dfrac{4}{17} \\
& S = \left\{\dfrac{4}{17}\right\} \\
& \\
& \text{7) } \dfrac{2(x - 4)}{4} - \dfrac{3 + 2x}{10} = \dfrac{4x + 1}{5} \\
& \dfrac{x - 4}{2} - \dfrac{3 + 2x}{10} = \dfrac{4x + 1}{5} \\
& \dfrac{5(x - 4)}{10} - \dfrac{3 + 2x}{10} = \dfrac{2(4x + 1)}{10} \\
& 5(x - 4) - (3 + 2x) = 2(4x + 1) \\
& 5x - 20 - 3 - 2x = 8x + 2 \\
& 3x - 23 = 8x + 2 \\
& 3x - 8x = 2 + 23 \\
& -5x = 25 \\
& x = -5 \\
& S = \{-5\} \\
& \\
& \text{8) } \dfrac{2x - 1}{3} - \dfrac{5 - 3x}{2} = \dfrac{x + 7}{4} \\
& \dfrac{4(2x - 1)}{12} - \dfrac{6(5 - 3x)}{12} = \dfrac{3(x + 7)}{12} \\
& 4(2x - 1) - 6(5 - 3x) = 3(x + 7) \\
& 8x - 4 - 30 + 18x = 3x + 21 \\
& 26x - 34 = 3x + 21 \\
& 26x - 3x = 21 + 34 \\
& 23x = 55 \\
& x = \dfrac{55}{23} \\
& S = \left\{\dfrac{55}{23}\right\} \\
& \\
& \text{9) } \dfrac{4 - 4x}{5} + 4 = \dfrac{x}{3} - \dfrac{x - 2}{2} \\
& \dfrac{6(4 - 4x)}{30} + \dfrac{120}{30} = \dfrac{10x}{30} - \dfrac{15(x - 2)}{30} \\
& 6(4 - 4x) + 120 = 10x - 15(x - 2) \\
& 24 - 24x + 120 = 10x - 15x + 30 \\
& -24x + 144 = -5x + 30 \\
& -24x + 5x = 30 - 144 \\
& -19x = -114 \\
& x = 6 \\
& S = \{6\} \\
& \\
& \text{10) } \dfrac{2x + 1}{4} - \dfrac{x - 5}{3} = \dfrac{4x - 1}{12} + 2 \\
& \dfrac{3(2x + 1)}{12} - \dfrac{4(x - 5)}{12} = \dfrac{4x - 1}{12} + \dfrac{24}{12} \\
& 3(2x + 1) - 4(x - 5) = 4x - 1 + 24 \\
& 6x + 3 - 4x + 20 = 4x + 23 \\
& 2x + 23 = 4x + 23 \\
& 2x - 4x = 23 - 23 \\
& -2x = 0 \\
& x = 0 \\
& S = \{0\}
\end{aligned}$