Question

Solve the equation. Check your solution.

$\mathbf{12}\mathbf{k}\mathbf{+}\mathbf{7}\mathbf{=}\mathbf{31}$

Short answer

The solution for the equation $12k+7=31$is$k=2$ .

Step-by-step solution

– Separate the variable and constants

Write the original equation and separate the variables.

$\begin{array}{c}12k+7=31\\ 12k=31-7\\ 12k=24\end{array}$

– Solve for k

Now, divide both sides of the equation by 12.

$\begin{array}{c}\frac{12k}{12}=\frac{24}{12}\\ k=2\end{array}$

Therefore, the solution of the equation is$k=2$ .

– Check the solution 

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

$12k+7=31$

Now, substitute $k=2$and check the result.

$\begin{array}{c}12\left(2\right)+7=31\\ 24+7=31\\ 31=31\end{array}$

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