a) \(x=\dfrac{1}{4}+\dfrac{2}{13}\)

\(x=\dfrac{13}{52}+\dfrac{8}{52}\)

⇒ \(x=\dfrac{21}{52}\)

b) \(\dfrac{x}{3}=\dfrac{2}{3}+\dfrac{-1}{7}\)

\(\dfrac{x}{3}=\dfrac{14}{21}+\dfrac{-3}{21}\)

\(\dfrac{x}{3}=\dfrac{11}{21}\)

⇒ \(x=\dfrac{11.3}{21}=\dfrac{33}{21}\)

⇒ \(x=\dfrac{11}{7}\)

c) \(\dfrac{-8}{3}+\dfrac{1}{3}< x< \dfrac{-2}{7}+\dfrac{-5}{7}\)

\(\dfrac{-17}{7}< x< -1\)

⇒ \(-17< x< -7\)

⇒ \(x\in\left\{-16;-15,-;-6\right\}\)

d) \(\dfrac{1}{6}+\dfrac{2}{5}\)

\(=\dfrac{5}{30}+\dfrac{12}{30}\)

\(=\dfrac{17}{30}\)

e) \(\dfrac{3}{5}+\dfrac{-7}{4}\)

\(=\dfrac{12}{20}+\dfrac{-35}{20}\)

\(=\dfrac{-23}{20}\)

f) \(\dfrac{4}{13}+\dfrac{-12}{30}\)

\(=\dfrac{4}{13}+\dfrac{-2}{5}\)

\(=\dfrac{20}{65}+\dfrac{-26}{65}\)

\(=\dfrac{-6}{65}\)

g) \(\dfrac{-3}{29}+\dfrac{16}{58}\)

\(=\dfrac{-6}{58}+\dfrac{16}{58}\)

\(=\dfrac{10}{58}\)

h) \(\dfrac{8}{40}+\dfrac{-36}{45}\)

\(=\dfrac{1}{5}+\dfrac{-4}{5}\)

\(=\dfrac{-3}{5}\)

j) \(\dfrac{-8}{18}+\dfrac{15}{27}\)

\(=\dfrac{-2}{9}+\dfrac{5}{9}\)

\(=\dfrac{3}{9}\)

\(=\dfrac{1}{3}\)