Question

\(a,-\dfrac{2}{3}.\left(x-\dfrac{1}{4}\right)=\dfrac{1}{3}.\left(2x-1\right)\)

\(b,\dfrac{1}{5}.2^x+\dfrac{1}{3}.2^{x+11}=\dfrac{1}{5}.2^7+\dfrac{1}{3}.2^8\)

\(c,\dfrac{x-19}{345}+\dfrac{x-20}{346}=\dfrac{x-1}{347}+\dfrac{x-22}{348}\)

Answer 1

a)

\(\dfrac{-2}{3}\cdot\left(x-\dfrac{1}{4}\right)=\dfrac{1}{3}\cdot\left(2x-1\right)\\ \dfrac{-2}{3}x-\left(\dfrac{-1}{6}\right)=\dfrac{2}{3}x-\dfrac{1}{3}\\ \dfrac{-2}{3}x+\dfrac{1}{6}=\dfrac{2}{3}x-\dfrac{1}{3}\\ \dfrac{-2}{3}x-\dfrac{2}{3}x=\dfrac{-1}{3}-\dfrac{1}{6}\\ -x\cdot\left(\dfrac{2}{3}+\dfrac{2}{3}\right)=\dfrac{-2}{6}-\dfrac{1}{6}\\ \dfrac{-4}{3}x=\dfrac{-1}{2}\\ x=\dfrac{-1}{2}:\dfrac{-4}{3}\\ x=\dfrac{-1}{2}\cdot\dfrac{-3}{4}\\ x=\dfrac{3}{8}\)