Question

Solve the equation. Check your solution.

$12=\frac{\mathrm{f}}{2}-8$

Short answer

The solution for the equation $12=\frac{f}{2}-8$ is $f=40$.

Step-by-step solution

– Separate the variable and constants

Write the original equation and separate the variables.

$\begin{array}{l}12=\frac{f}{2}-8\\ 12+8=\frac{f}{2}\\ 20=\frac{f}{2}\end{array}$

– Solve for f

Multiply both sides of the equation $20=\frac{f}{2}$ by 2 and simplify.

$\begin{array}{l}20\times 2=\frac{f}{2}\times 2\\ f=40\end{array}$

Therefore, the solution of the equation is $f=40$.

– Check the solution 

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

localid="1649207493077" $12=\frac{f}{2}-8$

Now, substitute $f=40$and check the result.

$$\begin{gathered} 12=\frac{40}{2}-8 \\ 12=20-8 \\ 12=12 \end{gathered}$$

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

$\begin{array}{l}12=\frac{40}{2}-8\\ 12=20-8\\ 12=12\end{array}$