# How do you solve -49/7=(a+7)/6?

Mar 7, 2017

See the entire solution process below:

#### Explanation:

First, factor the fraction on the left side of the equation:

$\frac{7 \times - 7}{7 \times 1} = \frac{a + 7}{6}$

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

$- \frac{7}{1} = \frac{a + 7}{6}$

$- 7 = \frac{a + 7}{6}$

Next, multiply each side of the equation by $\textcolor{red}{6}$ to eliminate the fraction while keeping the equation balanced:

$\textcolor{red}{6} \times - 7 = \textcolor{red}{6} \times \frac{a + 7}{6}$

$- 42 = \cancel{\textcolor{red}{6}} \times \frac{a + 7}{\textcolor{red}{\cancel{\textcolor{b l a c k}{6}}}}$

$- 42 = a + 7$

Now, subtract $\textcolor{red}{7}$ from each side of the equation to solve for $a$ while keeping the equation balanced:

$- 42 - \textcolor{red}{7} = a + 7 - \textcolor{red}{7}$

$- 49 = a + 0$

$- 49 = a$

$a = - 49$