Question

Solve the equation. Check your solution.

$\mathbf{4}\left(5-p\right)\mathbf{=}\mathbf{8}$

Short answer

The solution for the equation $4\left(5-p\right)=8$is $p=3$.

Step-by-step solution

– Separate the variable and constants

Write the original equation and separate the variable and constants.

$\begin{array}{c}4\left(5-p\right)=8\\ 20-4p=8\left[\text{distributiveproperty}\right]\\ 20-20-4p=8-20\left[\text{subtract20fromeachside}\right]\\ -4p=-12\end{array}$

– Solve for p

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

$\begin{array}{c}-4p÷\left(-4\right)=-12÷\left(-4\right)\\ p=3\end{array}$

Therefore, the solution of the equation is $p=3$.

– Check the solution 

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

$4\left(5-p\right)=8$

Now, substitute $p=3$and check the result.

$\begin{array}{c}4\left(5-3\right)=8\\ 4\left(2\right)=8\\ 8=8\end{array}$

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