Tìm x biết:

a) \(\frac{3}{5}x - \frac{1}{2} = \frac{1}{7}\)

b) $(4,5-2x).\frac{11}{7}=\frac{11}{14}$

c) \[80\% + \frac{7}{6}:x = \frac{1}{6}\]

d) \(\frac{3}{4} - \left( {4\frac{1}{2} + 3x} \right) = - 1\)

Hướng dẫn giải:

a) \(\frac{3}{5}x - \frac{1}{2} = \frac{1}{7}\)

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

\(\frac{3}{5}x = \frac{2}{{14}} + \frac{7}{{14}}\)

\(\frac{3}{5}x = \frac{9}{{14}}\)

\(x = \frac{9}{{14}}:\frac{3}{5}\)

\(x = \frac{9}{{14}}.\frac{5}{3}\)

\(x = \frac{{15}}{{14}}\)

Vậy \(x = \frac{{15}}{{14}}\).

b) \(\left( {4,5 - 2x} \right).\frac{{11}}{7} = \frac{{11}}{{14}}\)

\[\frac{9}{2} - 2x = \frac{{11}}{{14}}:\frac{{11}}{7}\]

\(\frac{9}{2} - 2x = \frac{{11}}{{14}}.\frac{7}{{11}}\)

\(\frac{9}{2} - 2x = \frac{1}{2}\)

\(2x = \frac{9}{2} - \frac{1}{2}\)

\(2x = \frac{8}{2}\)

2x = 4

x = 2.

Vậy x = 2.

c) \[80\% + \frac{7}{6}:x = \frac{1}{6}\]

\(\frac{{80}}{{100}} + \frac{7}{6} = \frac{1}{6}\)

\[\frac{4}{5} + \frac{7}{6}:x = \frac{1}{6}\]

\[\frac{7}{6}:x = \frac{1}{6} - \frac{4}{5}\]

\[\frac{7}{6}:x = \frac{5}{{30}} - \frac{{24}}{{30}}\]

\[\frac{7}{6}:x = \frac{{ - 19}}{{30}}\]      

\[x = \frac{7}{6}:\frac{{ - 19}}{{30}}\]

\(x = \frac{7}{6}.\frac{{30}}{{ - 19}}\)

\[x = \frac{{ - 35}}{{19}}\]

Vậy \[x = \frac{{ - 35}}{{19}}\].

d) \(\frac{3}{4} - \left( {4\frac{1}{2} + 3x} \right) = - 1\)

\(4\frac{1}{2} + 3x = \frac{3}{4} - \left( { - 1} \right)\)

\(\frac{9}{2} + 3x = \frac{3}{4} + 1\)

\(\frac{9}{2} + 3x = \frac{3}{4} + \frac{4}{4}\)

\(\frac{9}{2} + 3x = \frac{7}{4}\)

\(3x = \frac{9}{2} - \frac{7}{4}\)

\(3x = \frac{{18}}{4} - \frac{7}{4}\)

\(3x = \frac{{11}}{4}\)

\(x = \frac{{11}}{4}:3\)

\(x = \frac{{11}}{4}.\frac{1}{3}\)

\(x = \frac{{11}}{{12}}\)

Vậy \(x = \frac{{11}}{{12}}\).\(\)