# How do you solve (7/9)x-1/2=3?

Feb 8, 2017

See the entire solution process below:

#### Explanation:

First, multiply each side of the equation by $\textcolor{red}{18}$ to eliminate the fractions while keeping the equation balanced. Eliminating the fractions up front will make the problem easier to work with and $\textcolor{red}{18}$ is the least common denominator of the two fractions:

$\textcolor{red}{18} \left(\left(\frac{7}{9}\right) x - \frac{1}{2}\right) = \textcolor{red}{18} \times 3$

$\left(\textcolor{red}{18} \times \left(\frac{7}{9}\right) x\right) - \left(\textcolor{red}{18} \times \frac{1}{2}\right) = 54$

$\left(\cancel{\textcolor{red}{18}} 2 \times \left(\frac{7}{\textcolor{red}{\cancel{\textcolor{b l a c k}{9}}}}\right) x\right) - \left(\cancel{\textcolor{red}{18}} 9 \times \frac{1}{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}}}\right) = 54$

$14 x - 9 = 54$

Next, add $\textcolor{red}{9}$ to each side of the equation to isolate the $x$ term while keeping the equation balanced:

$14 x - 9 + \textcolor{red}{9} = 54 + \textcolor{red}{9}$

$14 x - 0 = 63$

$14 x = 63$

Now, divide each side of the equation by $\textcolor{red}{14}$ to solve for $x$ while keeping the equation balanced:

$\frac{14 x}{\textcolor{red}{14}} = \frac{63}{\textcolor{red}{14}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{14}}} x}{\cancel{\textcolor{red}{14}}} = \frac{7 \times 9}{7 \times 2}$

$x = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{7}}} \times 9}{\textcolor{red}{\cancel{\textcolor{b l a c k}{7}}} \times 2}$

$x = \frac{9}{2}$