Question

Solve the equation. Check your solution.

$\mathbf{12}\mathbf{=}\frac{\mathbf{a}}{\mathbf{36}}\mathbf{+}\mathbf{17}$

Short answer

The solution for the equation$12=\frac{a}{36}+17$is$a=-180$.

Step-by-step solution

.  Separate the variable and constants

Write the original equation and separate the variables.

$\begin{array}{l}12=\frac{a}{36}+17\\ 12-17=\frac{a}{36}\\ -5=\frac{a}{36}\end{array}$

.  Solve for a

Now, multiply both sides of the equation by 36.

$\begin{array}{l}-5\times 36=\frac{a}{36}\times 36\\ -180=a\\ a=-180\end{array}$

Therefore, the solution of the equation is $a=-180$.

.  Check the solution 

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

$12=\frac{a}{36}+17$

Now, substitute$a=-180$and check the result.

$\begin{array}{l}12=\frac{-180}{36}+17\\ 12=-5+17\\ 12=12\end{array}$

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