Question

Solve the equation. Check your solution.

$\mathbf{54}\mathbf{.}\mathbf{7}\mathbf{=}\mathbf{-}\mathbf{9}\mathbf{.}\mathbf{3}\mathbf{n}\mathbf{+}\mathbf{8}\mathbf{.}\mathbf{2}$

Short answer

The solution for the equation $54.7=-9.3n+8.2$is $n=-5$.

Step-by-step solution

.  Separate the variable and constants

Write the original equation and separate the variables.

$\begin{array}{l}54.7=-9.3n+8.2\\ 54.7-8.2=-9.3n\\ 46.5=-9.3n\end{array}$

.  Solve for n

Now, divide both sides of the equation by -9.3.

$\begin{array}{l}\frac{46.5}{-9.3}=\frac{-9.3n}{-9.3}\\ \frac{46.5}{-9.3}=n\\ -5=n\\ n=-5\end{array}$

Therefore, the solution of the equation is $n=-5$.

.  Check the solution 

To check the solution, write the original equation and substitute the value of n.

$54.7=-9.3n+8.2$

Now, substitute$n=-5$and check the result.

$\begin{array}{l}54.7=-9.3\left(-5\right)+8.2\\ 54.7=-9.3\left(-5\right)+8.2\\ 54.7=46.5+8.2\\ 54.7=54.7\end{array}$

As the left-hand side is equal to right hand side, this signifies that the solution is correct.

$\begin{array}{l}54.7=-9.3\left(-5\right)+8.2\\ 54.7=-9.3\left(-5\right)+8.2\\ 54.7=46.5+8.2\\ 54.7=54.7\end{array}$