Question

What value of y makes the equation 1/4-2/3y=3/4-1/3y true

Answer 1

`\cfrac{1}{4}-\cfrac{2}{3}y~~ = ~~\cfrac{3}{4}-\cfrac{1}{3}y\implies \cfrac{1}{4}-\cfrac{2y}{3}~~ = ~~\cfrac{3}{4}-\cfrac{y}{3} \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{12}}{12\left( \cfrac{1}{4}-\cfrac{2y}{3} \right)~~ = ~~12\left( \cfrac{3}{4}-\cfrac{y}{3} \right)}\implies 3-8y~~ = ~~9-4y\implies 3=9+4y \\\\\\ -6=4y\implies \cfrac{-6}{4}=y\implies \boxed{-\cfrac{3}{2}=y}`