Question

Solve the equation. Check your solution.

$\mathbf{-}\mathbf{2}\left(z+11\right)\mathbf{=}\mathbf{6}$

Short answer

The solution for the equation$-2\left(z+11\right)=6$ is$z=-14$ .

Step-by-step solution

– Separate the variable and constants

Write the original equation and separate the variable and constants.

$\begin{array}{c}\mathbf{-}\mathbf{2}\left(z+11\right)\mathbf{=}\mathbf{6}\\ \mathbf{-}\mathbf{2}\mathbf{z}\mathbf{-}\mathbf{22}\mathbf{=}\mathbf{6}\\ \mathbf{-}\mathbf{2}\mathbf{z}\mathbf{-}\mathbf{22}\mathbf{+}\mathbf{22}\mathbf{=}\mathbf{6}\mathbf{+}\mathbf{22}\\ \mathbf{-}\mathbf{2}\mathbf{z}\mathbf{=}\mathbf{28}\\ \mathbf{2}\mathbf{z}\mathbf{=}\mathbf{-}\mathbf{28}\end{array}$

– Solve for z

Now, divide both sides of the equation by 2.

$\begin{array}{c}\frac{2z}{2}=\frac{-28}{2}\\ z=-14\end{array}$

Therefore, the solution of the equation is $z=-14$.

– Check the solution 

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

$-2\left(z+11\right)=6$

Now, substitute $z=-14$and check the result.

$\begin{array}{c}-2\left(-14+11\right)=6\\ -2\left(-3\right)=6\\ 6=6\end{array}$

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