Tìm x của biểu thức sau, biết: a) 2/ 9 + 4 /5 x = 9/ 5 ; b) 5 /11 + 2/ 11 : ∣ ∣ 3/ 7 − x ∣ ∣ = 4 /5 .

a) \(\frac{2}{9} + \frac{4}{5}x = \frac{9}{5}\)

    \(\frac{4}{5}x = \frac{9}{5} - \frac{2}{9}\)

    \(\frac{4}{5}x = \frac{{71}}{{45}}\)

       \(x = \frac{{71}}{{45}}:\frac{4}{5}\)

       \(x = \frac{{71}}{{36}}\).

Vậy \(x = \frac{{71}}{{36}}\).

b) \(\frac{5}{{11}} + \frac{2}{{11}}:\left| {\frac{3}{7} - x} \right| = \frac{4}{5}\)

            \(\frac{2}{{11}}:\left| {\frac{3}{7} - x} \right| = \frac{4}{5} - \frac{5}{{11}}\)

            \(\frac{2}{{11}}:\left| {\frac{3}{7} - x} \right| = \frac{{19}}{{55}}\)

                  \(\left| {\frac{3}{7} - x} \right| = \frac{2}{{11}}:\frac{{19}}{{55}}\)

                  \(\left| {\frac{3}{7} - x} \right| = \frac{{10}}{{19}}\)

Trường hợp 1:

\(\frac{3}{7} - x = \frac{{10}}{{19}}\)

      \(x = \frac{3}{7} - \frac{{10}}{{19}}\)

      \(x =  - \frac{{13}}{{133}}\)

Vậy \(x \in \left\{ { - \frac{{13}}{{133}};\,\frac{{127}}{{133}}} \right\}\).

Trường hợp 2:

\(\frac{3}{7} - x =  - \frac{{10}}{{19}}\)

      \(x = \frac{3}{7} + \frac{{10}}{{19}}\)

      \(x = \frac{{127}}{{133}}\)