Question

Solve the equation. Check your solution.

$\mathbf{8}\left(\mathbf{z}\mathbf{+}\mathbf{4}\right)\mathbf{=}\mathbf{5}\left(\mathbf{13}\mathbf{+}\mathbf{z}\right)$

Short answer

The solution for the equation $8\left(z+4\right)=5\left(13+z\right)$ is $z=11$.

Step-by-step solution

– Separate the variable and constants

Write the original equation and separate the variable and constants.

$\begin{array}{c}8\left(z+4\right)=5\left(13+z\right)\\ 8z+32=65+5z\left(\text{Simplify}\right)\\ 8z-5z+32=65+5z-5z\left(\text{Subtract5zfrombothsides}\right)\\ 3z+32=65+0\left(\text{Simplify}\right)\\ 3z+32-32=65-32\left(\text{Subtract32frombothsides}\right)\\ 3z+0=33\left(\text{Simplify}\right)\end{array}$

– Solve for z

Now, divide both sides of the equation by 3.

$\begin{array}{c}\frac{3z}{3}=\frac{33}{3}\\ z=11\end{array}$

Therefore, the solution of the equation is $z=11$.

– Check the solution 

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

$8\left(z+4\right)=5\left(13+z\right)$

Now, substitute $z=11$ and check the result.

$\begin{array}{c}8\left(11+4\right)=5\left(13+11\right)\\ 8\left(15\right)=5\left(24\right)\\ 120=120\end{array}$

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