Question

X+3 2/5=2 1/6 what is x?

Answer 1

first off, let's convert the mixed fractions of 3⅖ and 2⅙ to improper, and then solve for x.

$\bf \stackrel{mixed}{3\frac{2}{5}}\implies \cfrac{3\cdot 5+2}{5}\implies \stackrel{improper}{\cfrac{17}{5}} \\[2em] \stackrel{mixed}{2\frac{1}{6}}\implies \cfrac{2\cdot 6+1}{6}\implies \stackrel{improper}{\cfrac{13}{6}}\\\\ \rule{31em}{0.25pt}\\\\ x+\cfrac{17}{5}=\cfrac{13}{6}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{30}}{30\left( x+\cfrac{17}{5} \right) =30\left( \cfrac{13}{6} \right)}\implies 30x+102=65 \\[2em] 30x=-37\implies x=-\cfrac{37}{30}\implies x=-1\frac{7}{30}$

if you're wondering why we multiply by the LCD of 30, is just to do away with the denominators.