Giải bài 6 trang 43 SGK Toán 6 Cánh diều

Đề bài

Tìm x, biết:

a) \(\frac{4}{7}.x - \frac{2}{3} = \frac{1}{5}\);

b) \(\frac{4}{5} + \frac{5}{7}:x = \frac{1}{6}\).

Lời giải chi tiết

a)

\(\begin{array}{l}\frac{4}{7}.x - \frac{2}{3} = \frac{1}{5}\\\frac{4}{7}.x = \frac{1}{5} + \frac{2}{3}\\\frac{4}{7}.x = \frac{3}{{15}} + \frac{{10}}{{15}}\\\frac{4}{7}.x = \frac{{13}}{{15}}\\x = \frac{{13}}{{15}}:\frac{4}{7}\\x = \frac{{13}}{{15}}.\frac{7}{4}\\x = \frac{{91}}{{60}}\end{array}\)

Vậy \(x = \frac{{91}}{{60}}\).

b)

\(\begin{array}{l}\frac{4}{5} + \frac{5}{7}:x = \frac{1}{6}\\\frac{5}{7}:x = \frac{1}{6} - \frac{4}{5}\\\frac{5}{7}:x = \frac{5}{{30}} - \frac{{24}}{{30}}\\\frac{5}{7}:x = \frac{{ - 19}}{{30}}\\x = \frac{5}{7}:\frac{{ - 19}}{{30}}\\x = \frac{5}{7}.\frac{{ - 30}}{{19}}\\x = \frac{{ - 150}}{{133}}\end{array}\)

Vậy \(x = \frac{{ - 150}}{{133}}\).