Tìm x của biểu thức, biết: a) 0 , 5 − x = − 5/ 14 ; b) ∣ ∣ 3x − 1/2 ∣ ∣ + 21/25 = 1 .

a) \(0,5 - x = \frac{{ - 5}}{{14}}\)

\(x = 0,5 - \frac{{ - 5}}{{14}}\)

\(x = \frac{1}{2} + \frac{5}{{14}}\)

\(x = \frac{7}{{14}} + \frac{5}{{14}} = \frac{{12}}{{14}}\)

\(x = \frac{6}{7}\)

Vậy \(x = \frac{6}{7}\).

b) \(\left| {3x - \frac{1}{2}} \right| + \frac{{21}}{{25}} = 1\).

\(\left| {3x - \frac{1}{2}} \right| = 1 - \frac{{21}}{{25}} = \frac{4}{{25}}\)

\(\left| {3x - \frac{1}{2}} \right| = {\left( {\frac{2}{5}} \right)^2} = {\left( { - \frac{2}{5}} \right)^2}\)

Suy ra \(3x - \frac{1}{2} = \frac{2}{5}\) hoặc \(3x - \frac{1}{2} = - \frac{2}{5}\)

Trường hợp 1:

\(3x - \frac{1}{2} = \frac{2}{5}\)

\(3x = \frac{2}{5} + \frac{1}{2} = \frac{4}{{10}} + \frac{5}{{10}}\)

\(3x = \frac{9}{{10}}\)

\(x = \frac{9}{{10}}:3 = \frac{9}{{10}}.\frac{1}{3}\)

\(x = \frac{3}{{10}}\).

Trường hợp 2:

\(3x - \frac{1}{2} = - \frac{2}{5}\)

\(3x = - \frac{2}{5} + \frac{1}{2} = \frac{{ - 4}}{{10}} + \frac{5}{{10}}\)

\(3x = \frac{1}{{10}}\)

\(x = \frac{1}{{10}}:3 = \frac{1}{{10}}.\frac{1}{3}\)

\(x = \frac{1}{{30}}\).

Vậy \[x \in \left\{ {\frac{3}{{10}};\frac{1}{{30}}} \right\}\].