Question

Solve the equation. Check your solution.

$\mathbf{-}\frac{\mathbf{x}}{\mathbf{2}}\mathbf{+}\mathbf{4}\mathbf{=}\mathbf{12}$

Short answer

The solution for the equation $-\frac{x}{2}+4=12$ is $x=-16$

Step-by-step solution

.  Separate the variable and constants

Write the original equation and separate the variables.

$\begin{array}{l}-\frac{x}{2}+4=12\\ -\frac{x}{2}=12-4\\ -\frac{x}{2}=8\end{array}$

.  Solve for x

Now, multiply both sides of the equation by 2.

$\begin{array}{l}-\frac{x}{2}\times 2=8\times 2\\ -x=16\\ x=-16\end{array}$

Therefore, the solution of the equation is$x=-16$

.  Check the solution 

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

$-\frac{x}{2}+4=12$

Now, substitute

$x=-16$

and check the result.

$\begin{array}{l}-\frac{\left(-16\right)}{2}+4=12\\ \frac{16}{2}+4=12\\ 8+4=12\\ 12=12\end{array}$

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