Question

Solve the equation. Check your solution.$\mathbf{-}\mathbf{5}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{25}(\mathbf{4}\mathbf{+}\mathbf{20}\mathbf{r})\mathbf{-}\mathbf{8}\mathbf{r}$

Short answer

The solution for the equation $-5=0.25(4+20r)-8r$is$r=2$ .

Step-by-step solution

– Separate the variable and constants

Write the original equation and separate the variable and constants.

$\begin{array}{c}-5=0.25(4+20r)-8r\\ -5=1+5r-8r\left[\text{distributiveproperty}\right]\\ -5=1-3r\left[\text{combineliketerms}\right]\\ -5-1=1-1-3r\left[\text{subtract1fromeachside}\right]\\ -6=-3r\end{array}$

– Solve for r

Now, divide both sides of the equation by -3.

$\begin{array}{c}-6÷(-3)=-3r÷(-3)\\ 2=r\\ r=2\end{array}$

Therefore, the solution of the equation is$r=2$ .

– Check the solution 

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

$-5=0.25(4+20r)-8r$

Now, substitute $r=2$and check the result.

$\begin{array}{c}-5=0.25(4+20r)-8r\\ -5=0.25(4+20\times 2)-8\times 2\\ -5=0.25(4+40)-16\\ -5=0.25\left(44\right)-16\\ -5=11-16\\ -5=-5\end{array}$

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