# How do you solve and check your solutions to c/5.3+8.3=11.3?

Jan 21, 2017

See the entire solution and validation process below:

#### Explanation:

To solve this problem, first subtract $\textcolor{red}{8.3}$ from each side of the equation to isolate the $c$ term while keeping the equation balanced:

$\frac{c}{5.3} + 8.3 - \textcolor{red}{8.3} = 11.3 - \textcolor{red}{8.3}$

$\frac{c}{5.3} + 0 = 3$

$\frac{c}{5.3} = 3$

Now, multiply each side of the equation by $\textcolor{red}{5.3}$ to solve for $c$ while keeping the equation balanced:

$\frac{c}{5.3} \times \textcolor{red}{5.3} = 3 \times \textcolor{red}{5.3}$

$\frac{c}{\textcolor{red}{\cancel{\textcolor{b l a c k}{5.3}}}} \times \cancel{\textcolor{red}{5.3}} = 15.9$

$c = 15.9$

To validate this solution, substitute $15.9$ for $c$ in the original equation and ensure the left side of the equation calculates out to $11.3$

$\frac{15.9}{5.3} + 8.3 = 11.3$

$3 + 8.3 = 11.3$

$11.3 = 11.3$