Giải Bài 4 trang 19 sách bài tập toán 7 tập 1 - Chân trời sáng tạo

Đề bài

Tìm x, biết:

a) \(x - \dfrac{3}{4} = \dfrac{2}{7}\)

b) \(- \dfrac{3}{8}x - 0,75 =  - 1\dfrac{1}{2}\)

c) \((0,25 - x):\dfrac{{ - 3}}{5} =  - \dfrac{3}{4}\)

d) \(\dfrac{{ - 3}}{5}.(4x - 1,2) =  - \dfrac{{12}}{{25}}\)

Lời giải chi tiết

a) \(x - \dfrac{3}{4} = \dfrac{2}{7}\)

\(\begin{array}{l}x = \dfrac{2}{7} + \dfrac{3}{4}\\ x = \dfrac{{8 + 21}}{{28}}\\ x = \dfrac{{29}}{{28}}\end{array}\)

Vậy \(x = \dfrac{{29}}{{28}}\)

b) \(- \dfrac{3}{8}x - 0,75 =  - 1\dfrac{1}{2}\)

\(   - \dfrac{3}{8}x - \dfrac{3}{4} =  - \dfrac{3}{2}\)

\(\begin{array}{l}   - \dfrac{3}{8}x =  - \dfrac{3}{2} + \dfrac{3}{4}\\   - \dfrac{3}{8}x =  - \dfrac{6}{4} + \dfrac{3}{4} = \dfrac{{ - 3}}{4}\\   - \dfrac{3}{8}x =  - \dfrac{3}{4}\\ x = \dfrac{3}{4}:\dfrac{3}{8} = 2\end{array}\)

Vậy \(x = 2\)

c) \((0,25 - x):\dfrac{{ - 3}}{5} =  - \dfrac{3}{4}\)

\(\begin{array}{l} \left( {\dfrac{1}{4} - x} \right).\dfrac{{ - 5}}{3} =  - \dfrac{3}{4}\\ \left( {\dfrac{1}{4} - x} \right) =  - \dfrac{3}{4}:\dfrac{{ - 5}}{3}\\ \left( {\dfrac{1}{4} - x} \right) =  - \dfrac{3}{4}.\dfrac{{ - 3}}{5}\\ \dfrac{1}{4} - x = \dfrac{9}{{20}}\\ x = \dfrac{1}{4} - \dfrac{9}{{20}} =  - \dfrac{1}{5}\end{array}\)

Vậy \(x =  - \dfrac{1}{5}\)

d) \(\dfrac{{ - 3}}{5}.(4x - 1,2) =  - \dfrac{{12}}{{25}}\)

\(\begin{array}{l}\dfrac{{ - 3}}{5}.\left( {4x - \dfrac{6}{5}} \right) =  - \dfrac{{12}}{{25}}\\ \left( {4x - \dfrac{6}{5}} \right) =  - \dfrac{{12}}{{25}}:\dfrac{{ - 3}}{5}\\ 4x - \dfrac{6}{5} =  - \dfrac{{12}}{{25}}.\dfrac{{ - 5}}{3}\\ 4x - \dfrac{6}{5} =  - \dfrac{{12}}{{25}}.\dfrac{{ - 5}}{3}\\ 4x - \dfrac{6}{5} = \dfrac{4}{5}\\ 4x = \dfrac{4}{5} + \dfrac{6}{5} = 2\\ x = \dfrac{1}{2}\end{array}\)

Vậy \(x = \dfrac{1}{2}\)