a) \(\left(-\dfrac{12}{27}+\dfrac{2}{3}\right)+=\dfrac{2}{9}< x< \left(\dfrac{11}{7}+\dfrac{2}{5}\right)+-\dfrac{7}{5}+\dfrac{3}{7}\)
\(\left(-\dfrac{12}{27}+\dfrac{2}{3}\right)+-\dfrac{2}{9}=-\dfrac{4}{9}+\dfrac{2}{3}+\dfrac{2}{9}\)
\(=\left(-\dfrac{4}{9}+-\dfrac{2}{9}\right)+\dfrac{2}{3}=-\dfrac{2}{3}+\dfrac{2}{3}=0\)
\(\left(\dfrac{11}{7}+\dfrac{2}{5}\right)+-\dfrac{7}{5}+\dfrac{3}{7}=\dfrac{11}{7}+\dfrac{2}{5}+-\dfrac{7}{5}+\dfrac{3}{7}\)
\(=\left(\dfrac{11}{7}+\dfrac{2}{5}\right)+\left(\dfrac{2}{5}+-\dfrac{7}{5}\right)=2+\left(-1\right)=1\)
→0<x<1 → x∈ 0,1).
b)\(\left(-\dfrac{8}{13}+\dfrac{7}{17}\right)+\dfrac{21}{13}< x< \left(-\dfrac{9}{14}+3\right)+\dfrac{5}{14}\)
\(\left(-\dfrac{8}{13}+\dfrac{7}{17}\right)+\dfrac{21}{13}=-\dfrac{8}{13}+\dfrac{7}{17}+\dfrac{21}{13}\)
\(=\left(-\dfrac{8}{13}+\dfrac{21}{13}\right)+\dfrac{7}{17}=1+\dfrac{7}{17}+\dfrac{17}{7}=\dfrac{24}{17}\)
\(\left(-\dfrac{9}{14}+3\right)+\dfrac{5}{-14}=-\dfrac{9}{14}+3+-\dfrac{5}{14}\)
\(\left(-\dfrac{9}{14}+-\dfrac{5}{14}\right)+3=\left(-1\right)+3=2\)
→\(\dfrac{24}{17}< x< 2\)→ x = 2.
