Question

Solve the equation. Check your solution.

$\mathbf{9}\mathbf{.}\mathbf{1}\mathbf{=}\frac{\mathbf{k}}{\mathbf{3}\mathbf{.}\mathbf{7}}\mathbf{+}\mathbf{4}\mathbf{.}\mathbf{1}$

Short answer

The solution for the equation $9.1=\frac{k}{3.7}+4.1$ is $k=18.5$.

Step-by-step solution

.  Separate the variable and constants

Write the original equation and separate the variables.

$\begin{array}{l}9.1=\frac{k}{3.7}+4.1\\ 9.1-4.1=\frac{k}{3.7}\\ 5=\frac{k}{3.7}\end{array}$

.  Solve for k

Now, multiply both sides of the equation by 3.7.

$\begin{array}{l}5\times 3.7=\frac{k}{3.7}\times 3.7\\ 5\times 3.7=k\\ k=18.5\end{array}$

Therefore, the solution of the equation is $k=18.5$.

.  Check the solution 

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

$3.2r+14.7=-6.74$

Now, substitute $k=18.5$and check the result.

$\begin{array}{l}9.1=\frac{18.5}{3.7}+4.1\\ 9.1=5+4.1\\ 9.1=9.1\end{array}$

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