Tìm \(x\), biết:

    a) \(0,75 - x =  - \frac{3}{5}\);                                           b) \(\frac{1}{3} + \frac{2}{3}x = 7,5\);                   c) \(\left( {x - \frac{4}{5}} \right)\left( {x + 2\frac{1}{5}} \right) = 0\).

a) \(0,75 - x =  - \frac{3}{5}\)

\(x = 0,75 - \left( { - \frac{3}{5}} \right)\)

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

\(x = \frac{{27}}{{20}}\)

Vậy \(x = \frac{{27}}{{20}}\).

b) \(\frac{1}{3} + \frac{2}{3}x = 7,5\)

\(\frac{2}{3}x = \frac{{15}}{2} - \frac{1}{3}\)

\(\frac{2}{3}x = \frac{{43}}{6}\)

\(x = \frac{{43}}{6}:\frac{2}{3}\)

\(x = \frac{{43}}{6}.\frac{3}{2}\)

\(x = \frac{{43}}{4}\)

Vậy \(x = \frac{{43}}{4}\).

c) \(\left( {x - \frac{4}{5}} \right)\left( {x + 2\frac{1}{5}} \right) = 0\)

Suy ra \(x - \frac{4}{5} = 0\) hoặc \(x + 2\frac{1}{5} = 0\)

Trường hợp 1:

\(x - \frac{4}{5} = 0\)

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

 Vậy \(x \in \left\{ {\frac{4}{5}; - \frac{{11}}{5}} \right\}\).

Trường hợp 2:

\(x + 2\frac{1}{5} = 0\)

\(x =  - 2\frac{1}{5}\)

\(x =  - \frac{{11}}{5}\)