Giải Bài 5 trang 18 sách bài tập toán 7 tập 1 - Chân trời sáng tạo

Đề bài

Tìm x, biết:

a) \(\dfrac{3}{4} + \dfrac{1}{9}:x = 0,5\)

b) \(\dfrac{3}{4} - \left( {x - \dfrac{2}{3}} \right) = 1\dfrac{1}{3}\)

c) \(\left( {\dfrac{5}{7} - x} \right).\dfrac{{11}}{{15}} = \dfrac{{ - 22}}{{45}}\)

d) \(\left( {2,5x - \dfrac{4}{7}} \right):\dfrac{8}{{21}} =  - 1,5\)

Lời giải chi tiết

\(\begin{array}{l}a)\dfrac{3}{4} + \dfrac{1}{9}:x = 0,5\\ \Leftrightarrow \dfrac{1}{9}:x = \dfrac{1}{2} - \dfrac{3}{4}\\ \Leftrightarrow \dfrac{1}{9}:x = \dfrac{{ - 1}}{4}\\ \Leftrightarrow x = \dfrac{1}{9}:\dfrac{{ - 1}}{4}\\ \Leftrightarrow x = \dfrac{{ - 4}}{9}\end{array}\)

Vậy \(x = \dfrac{{ - 4}}{9}\)

\(\begin{array}{l}b)\dfrac{3}{4} - \left( {x - \dfrac{2}{3}} \right) = 1\dfrac{1}{3}\\ \Leftrightarrow x - \dfrac{2}{3} = \dfrac{3}{4} - \dfrac{4}{3}\\ \Leftrightarrow x - \dfrac{2}{3} = \dfrac{{ - 7}}{{12}}\\ \Leftrightarrow x = \dfrac{{ - 7}}{{12}} + \dfrac{2}{3}\\ \Leftrightarrow x = \dfrac{1}{{12}}\end{array}\)

Vậy \(x = \dfrac{{ 1}}{12}\)

\(\begin{array}{l}c)\left( {\dfrac{5}{7} - x} \right).\dfrac{{11}}{{15}} = \dfrac{{ - 22}}{{45}}\\ \Leftrightarrow \dfrac{5}{7} - x = \dfrac{{ - 22}}{{45}}:\dfrac{{11}}{{15}}\end{array}\)

\(\begin{array}{l} \Leftrightarrow \dfrac{5}{7} - x = \dfrac{{ - 2}}{3}\\ \Leftrightarrow x = \dfrac{5}{7} - \left( {\dfrac{{ - 2}}{3}} \right)\end{array}\)

\(\begin{array}{l} \Leftrightarrow x = \dfrac{5}{7} + \dfrac{2}{3}\\\Leftrightarrow x = \dfrac{15}{21} + \dfrac{14}{21}\\ \Leftrightarrow x = \dfrac{{29}}{{21}}\end{array}\)

Vậy \(x = \dfrac{{ 29}}{21}\)

\(\begin{array}{l}d)\left( {2,5x - \dfrac{4}{7}} \right):\dfrac{8}{{21}} =  - 1,5\\ \Leftrightarrow \left( {\dfrac{5}{2}x - \dfrac{4}{7}} \right) = \dfrac{{ - 3}}{2}.\dfrac{8}{{21}}\\ \Leftrightarrow \dfrac{5}{2}x - \dfrac{4}{7} = \dfrac{{ - 4}}{7}\\ \Leftrightarrow \dfrac{5}{2}x = \dfrac{{ - 4}}{7} + \dfrac{4}{7}\\ \Leftrightarrow \dfrac{5}{2}x = 0\\ \Leftrightarrow x = 0\end{array}\)

Vậy \(x =0\)