Question

Solve the equation. Check your solution.$\mathbf{-}\mathbf{5}\mathbf{g}\mathbf{-}(\mathbf{8}\mathbf{-}\mathbf{g})\mathbf{=}\mathbf{12}$

Short answer

The solution for the equation$-5g-(8-g)=12$is$g=-5$.

Step-by-step solution

– Separate the variable and constants

Write the original equation and separate the variable and constants.

$\begin{array}{c}-5g-(8-g)=12\\ -5g-8+g=12\left[\text{distributiveproperty}\right]\\ -4g-8=12\left[\text{combineliketerms}\right]\\ -4g-8+8=12+8\left[\text{add8toeachside}\right]\\ -4g=20\end{array}$

– Solve for g

Now, divide both sides of the equation by -4.

$\begin{array}{c}-4g÷(-\text{4})=20÷(-\text{4})\\ g=-5\end{array}$

Therefore, the solution of the equation is$g=-5$.

– Check the solution 

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

$-5g-(8-g)=12$

Now, substitute $g=-5$and check the result.

$\begin{array}{c}-5(-5)-(8-(-5))=12\\ 25-(8+5)=12\\ 25-13=12\\ 12=12\end{array}$

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