Question

Solve the equation. Check your solution.

$\mathbf{13}\mathbf{-}\mathbf{3}\mathbf{p}\mathbf{=}\mathbf{-}\mathbf{5}\left(\mathbf{3}\mathbf{+}\mathbf{2}\mathbf{p}\right)$

Short answer

The solution for the equation $13-3p=-5\left(3+2p\right)$ is $p=-4$.

Step-by-step solution

– Separate the variable and constants

Write the original equation and separate the variable and constants.

$\begin{array}{c}13-3p=-5\left(3+2p\right)\\ 13-3p=-15-10p\left(\text{Usedistributiveproperty}\right)\\ 13+15-3p=-15+15-10p\left(\text{add15tobothsides}\right)\\ 28-3p=0-10p\left(\text{simplify}\right)\\ 28-3p+3p=-10p+3p\left(\text{add}3p\text{tobothsides}\right)\\ 28=-7p\left(\text{simplify}\right)\end{array}$

– Solve for p

Now, divide both sides of the equation by -7.

$\begin{array}{c}\frac{28}{-7}=\frac{-7p}{-7}\\ p=-4\end{array}$

Therefore, the solution of the equation is $p=-4$.

– Check the solution 

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

$13-3p=-5\left(3+2p\right)$

Now, substitute $p=-4$ and check the result.

$\begin{array}{c}13-3\left(-4\right)=-5\left(3+2\left(-4\right)\right)\\ 13+12=-5\left(3-8\right)\\ 25=-5\left(-5\right)\\ 25=25\end{array}$

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