Tìm số hữu tỉ x, biết:

a) \(\left| {x + \frac{1}{3}} \right| - 4 = - 1\).

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

Lời giải

a) \(\left| {x + \frac{1}{3}} \right| - 4 = - 1\)

\(\left| {x + \frac{1}{3}} \right| = 3\)

Trường hợp 1:

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

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

\(x = \frac{8}{3}\)

Trường hợp 2:

\(x + \frac{1}{3} = - 3\)

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

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

Vậy \(x \in \left\{ {\frac{8}{3};\frac{{ - 10}}{3}} \right\}\).

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

    \(\frac{7}{4}x + \frac{3}{2} = - \frac{4}{5}\)

    \(\frac{7}{4}x = - \frac{4}{5} - \frac{3}{2}\)

    \(\frac{7}{4}x = \frac{{ - 23}}{{10}}\)

    \(x = \frac{{ - 23}}{{10}}:\frac{7}{4}\)

    \(x = \frac{{ - 23}}{{10}}.\frac{4}{7}\)

    \(x = - \frac{{46}}{{35}}\)

Vậy \(x = - \frac{{46}}{{35}}\).