\(\frac{x-1}{2}+\frac{x-1}{4}=1-\frac{2\left(x-1\right)}{3}\)
\(\Leftrightarrow\left(x-1\right)\left(\frac{1}{2}+\frac{1}{4}+\frac{2}{3}\right)=1\)
\(\Leftrightarrow\left(x-1\right)\frac{17}{12}=1\)
\(\Leftrightarrow x-1=\frac{12}{17}\)
\(\Leftrightarrow x=\frac{29}{17}\)
Vậy phương trình có tập nghiệm là \(S=\left\{\frac{29}{17}\right\}\).
\(\frac{x-1}{2}+\frac{x-1}{4}=1-\frac{2\left(x-1\right)}{3}\)
\(\Leftrightarrow\frac{x-1}{2}+\frac{x-1}{4}=1-\frac{2x-2}{3}\)
\(\Leftrightarrow\frac{6\left(x-1\right)}{12}+\frac{3\left(x-1\right)}{12}=\frac{12}{12}-\frac{4\left(2x-2\right)}{12}\)
\(\Leftrightarrow6\left(x-1\right)+3\left(x-1\right)=12-4\left(2x-2\right)\)
\(\Leftrightarrow6x-6+3x-3=12-8x+8\)
\(\Leftrightarrow6x+3x+8x=12+8+6+3\)
\(\Leftrightarrow17x=29\)
\(\Leftrightarrow x=\frac{29}{17}\)
Vậy phương trình có nghiệm x=29/17
Đặt u = x - 1
Phương trình trở thành \(\frac{u}{2}+\frac{u}{4}=1-\frac{2u}{3}\)
\(\Leftrightarrow\frac{3u}{4}=\frac{3-2u}{3}\)
\(\Leftrightarrow9u=12-8u\Leftrightarrow17u=12\)
\(\Leftrightarrow u=\frac{12}{17}\Rightarrow x=\frac{12}{17}+1=\frac{29}{17}\)
Vậy phương trình có 1 nghiệm là \(\frac{29}{17}\)
\(\frac{x-1}{2}+\frac{x-1}{4}=4-\frac{2\left(x-1\right)}{3}\)
\(\Leftrightarrow\frac{3\left(x-1\right)}{4}=1-\frac{2\left(x-1\right)}{3}\)
\(\Leftrightarrow9\left(x-1\right)=12-8\left(x-1\right)\)
\(\Leftrightarrow9x-9=12-8x+8\)
\(\Leftrightarrow9x-9=-8x+20\)
\(\Leftrightarrow9x=-8x+20+9\)
\(\Leftrightarrow9x+8x=29\) (lam ngan gon)
\(\Leftrightarrow17x=29\)
\(\Leftrightarrow x=\frac{29}{17}\)
