Giải bài 5 trang 25 SGK Toán 7 tập 1 – Chân trời sáng tạo

Đề bài

Tìm x, biết:

a)\(\frac{2}{9}:x + \frac{5}{6} = 0,5;\)                        

b)\(\frac{3}{4} – \left( {x – \frac{2}{3}} \right) = 1\frac{1}{3};\)

c)\(1\frac{1}{4}:\left( {x – \frac{2}{3}} \right) = 0,75;\)                

d)\(\left( { – \frac{5}{6}x + \frac{5}{4}} \right):\frac{3}{2} = \frac{4}{3}\).

Lời giải chi tiết

a)

\(\begin{array}{l}\frac{2}{9}:x + \frac{5}{6} = 0,5\\\frac{2}{9}:x = \frac{1}{2} – \frac{5}{6}\\\frac{2}{9}:x = \frac{3}{6} – \frac{5}{6}\\\frac{2}{9}:x = \frac{{ – 2}}{6}\\x = \frac{2}{9}:\frac{{ – 2}}{6}\\x = \frac{2}{9}.\frac{{ – 6}}{2}\\x = \frac{{ – 2}}{3}\end{array}\)                        

Vậy \(x = \frac{{ – 2}}{3}\).

b)

\(\begin{array}{l}\frac{3}{4} – \left( {x – \frac{2}{3}} \right) = 1\frac{1}{3}\\x – \frac{2}{3} = \frac{3}{4} – 1\frac{1}{3}\\x – \frac{2}{3} = \frac{3}{4} – \frac{4}{3}\\x – \frac{2}{3} = \frac{9}{{12}} – \frac{{16}}{{12}}\\x – \frac{2}{3} = \frac{{ – 7}}{{12}}\\x = \frac{{ – 7}}{{12}} + \frac{2}{3}\\x = \frac{{ – 7}}{{12}} + \frac{8}{{12}}\\x = \frac{1}{12}\end{array}\)

Vậy\(x = \frac{1}{12}\).

c)

\(\begin{array}{l}1\frac{1}{4}:\left( {x – \frac{2}{3}} \right) = 0,75\\\frac{5}{4}:\left( {x – \frac{2}{3}} \right) = \frac{3}{4}\\x – \frac{2}{3} = \frac{5}{4}:\frac{3}{4}\\x – \frac{2}{3} = \frac{5}{4}.\frac{4}{3}\\x – \frac{2}{3} = \frac{5}{3}\\x = \frac{5}{3} + \frac{2}{3}\\x = \frac{7}{3}\end{array}\)               

Vậy \(x = \frac{7}{3}\).

d)

\(\begin{array}{l}\left( { – \frac{5}{6}x + \frac{5}{4}} \right):\frac{3}{2} = \frac{4}{3}\\ – \frac{5}{6}x + \frac{5}{4} = \frac{4}{3}.\frac{3}{2}\\ – \frac{5}{6}x + \frac{5}{4} = 2\\ – \frac{5}{6}x = 2 – \frac{5}{4}\\ – \frac{5}{6}x = \frac{8}{4} – \frac{5}{4}\\ – \frac{5}{6}x = \frac{3}{4}\\x = \frac{3}{4}:\left( { – \frac{5}{6}} \right)\\x = \frac{3}{4}.\frac{{ – 6}}{5}\\x = \frac{{ – 9}}{{10}}\end{array}\)

Vậy \(x = \frac{{ – 9}}{{10}}\).