Question

12x - 2/3 = 83 1/3
Can you please help me solve to find X?

Answer 1

let's firstly convert the mixed fraction to an improper fraction, and then let's multiply both sides by the LCD of all denominators

`\stackrel{mixed}{83(1)/(3)}\implies \cfrac{83\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{250}{3}} \\\\[-0.35em] ~\dotfill\\\\ 12x-\cfrac{2}{3}=\cfrac{250}{3}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{3\left( 12x-\cfrac{2}{3} \right)=3\left( \cfrac{250}{3} \right)}\implies 36x-2=250 \\\\\\ 36x=252\implies x=\cfrac{252}{36}\implies x=7`