Question

Solve the equation. Check your solution.$\mathbf{-}\mathbf{40}\mathbf{-}(\mathbf{2}\mathbf{x}\mathbf{+}\mathbf{5})\mathbf{=}\mathbf{-}\mathbf{61}$

Short answer

The solution for the equation $-40-(2x+5)=-61$is$x=8$ .

Step-by-step solution

– Separate the variable and constants

Write the original equation and separate the variable and constants.

$\begin{array}{c}-40-(2x+5)=-61\\ -40-2x-5=-61\left[\text{distributiveproperty}\right]\\ -2x-45=-61\left[\text{combineliketerms}\right]\\ -2x-45+45=-61+45\left[\text{add45toeachside}\right]\\ -2x=-16\end{array}$

– Solve for x

Now, divide both sides of the equation by -2.

$\begin{array}{c}-2x÷(-2)=-16÷(-2)\\ x=8\end{array}$

Therefore, the solution of the equation is$x=8$.

– Check the solution 

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

$-40-(2x+5)=-61$

Now, substitute $x=8$and check the result.

$\begin{array}{c}-40-(2\times 8+5)=-61\\ -40-(16+5)=-61\\ -40-21=-61\\ -61=-61\end{array}$

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