How do you solve and check your solutions to -5.3=2.2v-8.6?

Jan 31, 2017

See the entire solution and validation process below:

Explanation:

First, add $\textcolor{red}{8.6}$ to the equation to isolate the $v$ term while keeping the equation balanced:

$- 5.3 + \textcolor{red}{8.6} = 2.2 v - 8.6 + \textcolor{red}{8.6}$

$3.3 = 2.2 v - 0$

$3.3 = 2.2 v$

Now, divide each side of the equation by $\textcolor{red}{2.2}$ to solve for $v$ while keeping the equation balanced:

$\frac{3.3}{\textcolor{red}{2.2}} = \frac{2.2 v}{\textcolor{red}{2.2}}$

$\frac{3 \times 1.1}{2 \times 1.1} = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2.2}}} v}{\cancel{\textcolor{red}{2.2}}}$

$\frac{3 \times \cancel{1.1}}{2 \times \cancel{1.1}} = v$

$\frac{3}{2} = v$

$v = \frac{3}{2}$

Now to check the solution substitute $\frac{3}{2}$ for $v$ and calculate the right side of the equation and ensure it is equal $- 5.3$

$- 5.3 = \left(2.2 \times \frac{3}{2}\right) - 8.6$

$- 5.3 = 3.3 - 8.6$

$- 5.3 = - 5.3$

Because both sides of the equation are equal $v = \frac{3}{2}$ is a valid solution.