# How do you solve x/6 = x/7 + 5?

Apr 16, 2017

See the entire solution process below:

#### Explanation:

First, multiply each side of the equation by $\textcolor{red}{42}$ to eliminate the fractions while keeping the equation balanced. $\textcolor{red}{42}$ (or $7 \times 6$) is the Least Common Denominator for the two fractions:

$\textcolor{red}{42} \times \frac{x}{6} = \textcolor{red}{42} \left(\frac{x}{7} + 5\right)$

$\cancel{\textcolor{red}{42}} 7 \times \frac{x}{\textcolor{red}{\cancel{\textcolor{b l a c k}{6}}}} = \left(\textcolor{red}{42} \times \frac{x}{7}\right) + \left(\textcolor{red}{42} \times 5\right)$

$7 x = \left(\cancel{\textcolor{red}{42}} 6 \times \frac{x}{\textcolor{red}{\cancel{\textcolor{b l a c k}{7}}}}\right) + 210$

$7 x = 6 x + 210$

Now, subtract $\textcolor{red}{6 x}$ from each side of the equation to solve for $x$ while keeping the equation balanced:

$- \textcolor{red}{6 x} + 7 x = - \textcolor{red}{6 x} + 6 x + 210$

$\left(- \textcolor{red}{6} + 7\right) x = 0 + 210$

$1 x = 210$

$x = 210$