Question

Solve the equation. Check your solution.

$\mathbf{-}\mathbf{5}\left(2w+1\right)\mathbf{=}\mathbf{25}$

Short answer

The solution for the equation$-5\left(2w+1\right)=25$is$w=-3$.

Step-by-step solution

– Separate the variable and constants

Write the original equation and separate the variable and constants.

$\begin{array}{c}-5\left(2w+1\right)=25\\ -10w-5=25\left[\text{distributiveproperty}\right]\\ -10w-5+5=25+5\left[\text{add5toeachside}\right]\\ -10w=30\end{array}$

– Solve for w

Now, divide both sides of the equation by 10.

$\begin{array}{c}\frac{-10w}{10}=\frac{30}{10}\\ -w=3\\ w=-3\end{array}$

Therefore, the solution of the equation is $w=-3$.

– Check the solution 

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

$12=3\left(m-17\right)$

Now, substitute $w=-3$and check the result.

$\begin{array}{c}-5\left(2\left(-3\right)+1\right)=25\\ -5\left(-6+1\right)=25\\ -5\left(-5\right)=25\\ 25=25\end{array}$

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