a) \( 5(3x + 2) = 4x + 11 \)

\[
15x + 10 = 4x + 11 \\
15x - 4x = 11 - 10 \\
11x = 1 \\
{x = \dfrac{1}{11}}
\]

b) \( 1 - \dfrac{x}{4} - \dfrac{x + 2}{2} = 11x + 8 \)

Tìm mẫu chung là 4:
\[
1 - \dfrac{x}{4} - \dfrac{2(x + 2)}{4} = 11x + 8 \\
1 - \dfrac{x + 2(x + 2)}{4} = 11x + 8 \\
1 - \dfrac{x + 2x + 4}{4} = 11x + 8 \\
1 - \dfrac{3x + 4}{4} = 11x + 8 \\
\Rightarrow \dfrac{4 - 3x - 4}{4} = 11x + 8 - 1 \\
- \dfrac{3x}{4} = 11x + 7 \\
Nhân 4: -3x = 44x + 28 \\
-3x - 44x = 28 \Rightarrow -47x = 28 \Rightarrow {x = -\dfrac{28}{47}}
\]

c) \( x - \dfrac{1}{2} - \dfrac{x + 2}{3} = -4 \)

Mẫu chung là 6:
\[
\Rightarrow x - \dfrac{3}{6} - \dfrac{2(x + 2)}{6} = -4 \\
\Rightarrow x - \dfrac{3 + 2x + 4}{6} = -4 \\
\Rightarrow x - \dfrac{2x + 7}{6} = -4 \\
\Rightarrow \dfrac{6x - 2x - 7}{6} = -4 \\
\Rightarrow \dfrac{4x - 7}{6} = -4 \\
\Rightarrow 4x - 7 = -24 \Rightarrow 4x = -17 \Rightarrow {x = -\dfrac{17}{4}}
\]

d) \( x - \dfrac{1}{3} - \dfrac{2x + 3}{2} = 1 \)

Mẫu chung là 6:
\[
x - \dfrac{2}{6} - \dfrac{3(2x + 3)}{6} = 1 \\
x - \dfrac{2 + 6x + 9}{6} = 1 \\
x - \dfrac{6x + 11}{6} = 1 \\
\Rightarrow \dfrac{6x - 6x - 11}{6} = 1 \Rightarrow \dfrac{-11}{6} = 1 \quad \text{(vô lý)}
\Rightarrow {\text{Phương trình vô nghiệm}}
\]

e) \( 1 - \dfrac{x}{3} - \dfrac{x + 2}{2} = \dfrac{11x + 30}{6} \)

Mẫu chung là 6:
\[
1 - \dfrac{2x}{6} - \dfrac{3(x + 2)}{6} = \dfrac{11x + 30}{6} \\
\Rightarrow 1 - \dfrac{2x + 3x + 6}{6} = \dfrac{11x + 30}{6} \\
\Rightarrow 1 - \dfrac{5x + 6}{6} = \dfrac{11x + 30}{6} \\
\Rightarrow \dfrac{6 - 5x - 6}{6} = \dfrac{11x + 30}{6} \\
\Rightarrow \dfrac{-5x}{6} = \dfrac{11x + 30}{6} \\
\Rightarrow -5x = 11x + 30 \Rightarrow -16x = 30 \Rightarrow {x = -\dfrac{15}{8}}
\]