# How do you solve 2x-4/7=1/2x+9/14?

Feb 15, 2017

See the entire solution process below:

#### Explanation:

First, multiply each side of the equation by $\textcolor{red}{14}$ to eliminate the fractions while keeping the equation balanced. It will be easier to solve the equation without fractions and $\textcolor{red}{14}$ is the lowest common denominator for the three fractions:

$\textcolor{red}{14} \left(2 x - \frac{4}{7}\right) = \textcolor{red}{14} \left(\frac{1}{2} x + \frac{9}{14}\right)$

$\left(\textcolor{red}{14} \times 2 x\right) - \left(\textcolor{red}{14} \times \frac{4}{7}\right) = \left(\textcolor{red}{14} \times \frac{1}{2} x\right) + \left(\textcolor{red}{14} \times \frac{9}{14}\right)$

$28 x - \left(\cancel{\textcolor{red}{14}} 2 \times \frac{4}{\textcolor{red}{\cancel{\textcolor{b l a c k}{7}}}}\right) = \left(\cancel{\textcolor{red}{14}} 7 \times \frac{1}{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}}} x\right) + \left(\cancel{\textcolor{red}{14}} \times \frac{9}{\textcolor{red}{\cancel{\textcolor{b l a c k}{14}}}}\right)$

$28 x - 8 = 7 x + 9$

Next, add $\textcolor{red}{8}$ and subtract $\textcolor{b l u e}{7 x}$ from each side of the equation to isolate the $x$ term while keeping the equation balanced:

$28 x - 8 + \textcolor{red}{8} - \textcolor{b l u e}{7 x} = 7 x + 9 + \textcolor{red}{8} - \textcolor{b l u e}{7 x}$

$28 x - \textcolor{b l u e}{7 x} - 8 + \textcolor{red}{8} = 7 x - \textcolor{b l u e}{7 x} + 9 + \textcolor{red}{8}$

$28 x - \textcolor{b l u e}{7 x} - 8 + \textcolor{red}{8} = 7 x - \textcolor{b l u e}{7 x} + 9 + \textcolor{red}{8}$

$21 x - 0 = 0 + 17$

$21 x = 17$

Now, divide each side of the equation by $\textcolor{red}{21}$ to solve for $x$ while keeping the equation balanced:

$\frac{21 x}{\textcolor{red}{21}} = \frac{17}{\textcolor{red}{21}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{21}}} x}{\cancel{\textcolor{red}{21}}} = \frac{17}{21}$

$x = \frac{17}{21}$