Question

Solve the equation. Check your solution.

$\frac{\mathrm{b}}{4}-8=1$

Short answer

The solution for the equation $\frac{b}{4}-8=1$ is $b=36$.

Step-by-step solution

Step 1.  Separate the variables and constants

Write the original equation and separate the variables.

$\begin{array}{c}\frac{b}{4}-8=1\\ \frac{b}{4}=8+1\\ \frac{b}{4}=9\end{array}$

Step 2.  Solve for n

Multiply both sides of the equation $\frac{b}{4}=9$ by 4 and simplify.

$\begin{array}{c}\frac{b}{4}\times =9\times 4\\ b=9\times 4\\ b=36\end{array}$

Therefore, the solution of the equation is $b=36$.

Step 3.  Check the solution 

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

$\frac{b}{4}-8=1$

Now, substitute $b=36$and check the result.

$\begin{array}{c}\frac{36}{4}-8=1\\ \frac{36}{4}-8=1\\ 9-8=1\\ 1=1\end{array}$

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