# How do you solve \frac { x + 3} { 2} + \frac { 2x } { 7} = 7?

Jun 20, 2018

See a solution process below:

#### Explanation:

First, multiply each side of the equation by $\textcolor{red}{14}$ to eliminate the fractions while keeping the equation balanced. $\textcolor{red}{14}$ is the Least Common Denominator for the two fractions:

$\textcolor{red}{14} \left(\frac{x + 3}{2} + \frac{2 x}{7}\right) = \textcolor{red}{14} \times 7$

$\left(\textcolor{red}{14} \times \frac{x + 3}{2}\right) + \left(\textcolor{red}{14} \times \frac{2 x}{7}\right) = 98$

$\left(\cancel{\textcolor{red}{14}} 7 \times \frac{x + 3}{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}}}\right) + \left(\cancel{\textcolor{red}{14}} 2 \times \frac{2 x}{\textcolor{red}{\cancel{\textcolor{b l a c k}{7}}}}\right) = 98$

$7 \left(x + 3\right) + 4 x = 98$

$\left(7 \times x\right) + \left(7 \times 3\right) + 4 x = 98$

$7 x + 21 + 4 x = 98$

Next, we can group and combine like terms on the left side of the equation:

$7 x + 4 x + 21 = 98$

$\left(7 + 4\right) x + 21 = 98$

$11 x + 21 = 98$

Then, subtract $\textcolor{red}{21}$ from each side of the equation to isolate the $x$ term while keeping the equation balanced:

$11 x + 21 - \textcolor{red}{21} = 98 - \textcolor{red}{21}$

$11 x + 0 = 77$

$11 x = 77$

Now, divide each side of the equation by $\textcolor{red}{11}$ to solve for $x$ while keeping the equation balanced:

$\frac{11 x}{\textcolor{red}{11}} = \frac{77}{\textcolor{red}{11}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{11}}} x}{\cancel{\textcolor{red}{11}}} = 7$

$x = 7$