# How do you solve 1/3x+2=5/6?

Feb 26, 2017

See the entire solution process below:

#### Explanation:

First, subtract $\textcolor{red}{2}$ from each side of the equation to isolate the $x$ term while keeping the equation balanced:

$\frac{1}{3} x + 2 = \frac{5}{6}$

$\frac{1}{3} x + 2 - \textcolor{red}{2} = \frac{5}{6} - \textcolor{red}{2}$

$\frac{1}{3} x + 0 = \frac{5}{6} - \left(\frac{6}{6} \times \textcolor{red}{2}\right)$

$\frac{1}{3} x = \frac{5}{6} - \frac{12}{6}$

$\frac{1}{3} x = - \frac{7}{6}$

Now, multiply each side of the equation by $\textcolor{red}{3}$ to solve for $x$ while keeping the equation balanced:

$\textcolor{red}{3} \times \frac{1}{3} x = \textcolor{red}{3} \times - \frac{7}{6}$

$\cancel{\textcolor{red}{3}} \times \frac{1}{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}}} x = \cancel{\textcolor{red}{3}} \times - \frac{7}{\textcolor{red}{\cancel{\textcolor{b l a c k}{6}}} 2}$

$x = - \frac{7}{2}$

Feb 26, 2017

$x = - \frac{7}{2}$ or $3 \frac{1}{2}$

#### Explanation:

$\frac{1}{3} x + 2 = \frac{5}{6}$

$\therefore \frac{x}{3} + \frac{2}{1} = \frac{5}{6}$

$\therefore \frac{2 x + 12 = 5}{6}$

$\therefore \frac{2 x}{6} + \frac{12}{6} = \frac{5}{6}$

multiply L.H.S. and R.H.S by 6

$\therefore 2 x + 12 = 5$

$\therefore 2 x = 5 - 12$

$\therefore 2 x = - 7$

$x = - \frac{7}{2}$

substitute $x = - \frac{7}{2}$

$\therefore \frac{1}{3} \left(- \frac{7}{2}\right) + 2 = \frac{5}{6}$

$\therefore - \frac{7}{6} + \frac{12}{6} = \frac{5}{6}$

$\therefore \frac{5}{6} = \frac{5}{6}$