a) \(\left(\dfrac{3}{15}-x\right).\dfrac{1}{3}=\dfrac{2}{5}\)
\(\dfrac{1}{5}-x=\dfrac{2}{5}:\dfrac{1}{3}\)
\(\dfrac{1}{5}-x=\dfrac{6}{5}\)
\(x=\dfrac{1}{5}-\dfrac{6}{5}\)
\(x=-1\)
b) \(\dfrac{3}{5}.x-\dfrac{1}{3}=\dfrac{1}{4}\)
\(\dfrac{3}{5}.x=\dfrac{1}{4}+\dfrac{1}{3}\)
\(\dfrac{3}{5}.x=\dfrac{7}{12}\)
\(x=\dfrac{7}{12}:\dfrac{3}{5}\)
\(x=\dfrac{35}{36}\)
c) \(\dfrac{1}{4}+\dfrac{3}{4}:x=-2\)
\(\dfrac{3}{4}:x=-2-\dfrac{1}{4}\)
\(\dfrac{3}{4}:x=-\dfrac{9}{4}\)
\(x=-\dfrac{9}{4}:\dfrac{3}{4}\)
\(x=-3\)
d) Giống câu a đã giải
e) \(2.\left(\dfrac{1}{2}x-\dfrac{1}{3}\right)-\dfrac{3}{2}=\dfrac{1}{4}\)
\(x-\dfrac{2}{3}=\dfrac{1}{4}+\dfrac{3}{2}\)
\(x-\dfrac{2}{3}=\dfrac{7}{4}\)
\(x=\dfrac{7}{4}+\dfrac{2}{3}\)
\(x=\dfrac{29}{12}\)
f) \(\left(\dfrac{1}{2}+2x\right)\left(2x-3\right)=0\)
\(\Rightarrow\dfrac{1}{2}+2x=0\) hoặc \(2x-3=0\)
*) \(\dfrac{1}{2}+2x=0\)
\(2x=-\dfrac{1}{2}\)
\(x=-\dfrac{1}{2}:2\)
\(x=-\dfrac{1}{4}\)
*) \(2x-3=0\)
\(2x=3\)
\(x=\dfrac{3}{2}\)
Vậy \(x=-\dfrac{1}{4};x=\dfrac{3}{2}\)
g) \(\left(4x-5\right)\left(\dfrac{4}{5}x-2\right)=0\)
\(\Rightarrow4x-5=0\) hoặc \(\dfrac{4}{5}x-2=0\)
*) \(4x-5=0\)
\(4x=5\)
\(x=\dfrac{5}{4}\)
*) \(\dfrac{4}{5}x-2=0\)
\(\dfrac{4}{5}x=2\)
\(x=2:\dfrac{4}{5}\)
\(x=\dfrac{5}{2}\)
Vậy \(x=\dfrac{5}{4};x=\dfrac{5}{2}\)
h) \(\dfrac{1}{4}-\left(2x+\dfrac{1}{2}\right)^2=0\)
\(\left(2x+\dfrac{1}{2}\right)^2=\dfrac{1}{4}\)
\(\Rightarrow2x+\dfrac{1}{2}=-\dfrac{1}{2}\) hoặc \(2x+\dfrac{1}{2}=\dfrac{1}{2}\)
*) \(2x+\dfrac{1}{2}=-\dfrac{1}{2}\)
\(2x=-\dfrac{1}{2}-\dfrac{1}{2}\)
\(2x=-1\)
\(x=-\dfrac{1}{2}\)
*) \(2x+\dfrac{1}{2}=\dfrac{1}{2}\)
\(2x=\dfrac{1}{2}-\dfrac{1}{2}\)
\(2x=0\)
\(x=0\)
Vậy \(x=-1;x=0\)
i) \(25.\left(3x-\dfrac{1}{2}\right)^2=16\)
\(\left(3x-\dfrac{1}{2}\right)^2=\dfrac{16}{25}\)
\(\Rightarrow3x-\dfrac{1}{2}=-\dfrac{4}{5}\) hoặc \(3x-\dfrac{1}{2}=\dfrac{4}{5}\)
*) \(3x-\dfrac{1}{2}=-\dfrac{4}{5}\)
\(3x=-\dfrac{4}{5}+\dfrac{1}{2}\)
\(3x=-\dfrac{3}{10}\)
\(x=-\dfrac{3}{10}:3\)
\(x=-\dfrac{1}{10}\)
*) \(3x-\dfrac{1}{2}=\dfrac{4}{5}\)
\(3x=\dfrac{4}{5}+\dfrac{1}{2}\)
\(3x=\dfrac{13}{10}\)
\(x=\dfrac{13}{10}:3\)
\(x=\dfrac{13}{30}\)
Vậy \(x=-\dfrac{1}{10};x=\dfrac{13}{30}\)
