Question

Solve the equation. Check your solution.$\mathbf{-}\mathbf{3}(\mathbf{2}\mathbf{z}\mathbf{-}\mathbf{8})\mathbf{+}\mathbf{10}\mathbf{z}\mathbf{=}\mathbf{16}$

Short answer

The solution for the equation $-3(2z-8)+10z=16$is$z=-2$ .

Step-by-step solution

– Separate the variable and constants

Write the original equation and separate the variable and constants.

$\begin{array}{c}-3(2z-8)+10z=16\\ -6z+24+10z=16\left[\text{distributiveproperty}\right]\\ 4z+24=16\left[\text{combineliketerms}\right]\\ 4z+24-24=16-24\left[\text{subtractfrom24toeachside}\right]\\ 4z=-8\end{array}$

– Solve for z

Now, divide both sides of the equation by 4.

$\begin{array}{c}\text{4z}÷4=(-8)÷4\\ z=-2\end{array}$

Therefore, the solution of the equation is$z=-2$.

– Check the solution 

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

$-3(2z-8)+10z=16$

Now, substitute $z=-2$and check the result.

$\begin{array}{c}-3(2(-2)-8)+10(-2)=16\\ -3(-4-8)-20=16\\ -3(-12)-20=16\\ 36-20=16\\ 16=16\end{array}$

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