Question

1,3x−1/4+6x−2/8=1−3x/6

2,(2x−1)^2+(x−3)(2x−1)=0

Answer 1

\(1,\dfrac{3x-1}{4}+\dfrac{6x-2}{8}=\dfrac{1-3x}{6}\\ \Leftrightarrow1,\dfrac{3x-1}{4}+\dfrac{3x-1}{4}=\dfrac{1-3x}{6}\\ \Leftrightarrow2.\dfrac{3x-1}{4}=\dfrac{1-3x}{6}\\ \Leftrightarrow\dfrac{3x-1}{4}=\dfrac{1-3x}{12}\\ \Leftrightarrow12\left(3x-1\right)=4\left(1-3x\right)\\ \Leftrightarrow3\left(3x-1\right)=1-3x\\ \Leftrightarrow9x-3-1+3x=0\\ \Leftrightarrow12x-4=0\\ \Leftrightarrow x=\dfrac{1}{3}\)

\(2,\left(2x-1\right)^2+\left(x-3\right)\left(2x-1\right)=0\\ \Leftrightarrow\left(2x-1\right)\left(2x-1+x-3\right)=0\\ \Leftrightarrow\left(2x-1\right)\left(3x-4\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{2}\\x=\dfrac{4}{3}\end{matrix}\right.\)