Question

Solve the equation. Check your solution.

$\mathbf{2}\left(\mathbf{-}\mathbf{4}\mathbf{h}\mathbf{-}\mathbf{13}\right)\mathbf{=}\mathbf{37}\mathbf{+}\mathbf{13}\mathbf{h}$

Short answer

The solution for the equation $2\left(-4h-13\right)=37+13h$ is $h=-3$.

Step-by-step solution

– Separate the variable and constants

Write the original equation and separate the variable and constants.

$\begin{array}{c}2\left(-4h-13\right)=37+13h\\ -8h-26=37+13h\\ -8h-13h-26=37+13h-13h\left(\text{Subtract}13h\text{frombothsides}\right)\\ -21h-26=37\\ -21h-26-37=37-37\left(\text{Subtract37frombothsides}\right)\\ -21h-63=0\\ -21h=63\end{array}$

– Solve for h

Now, divide both sides of the equation by -21.

$\begin{array}{c}\frac{-21h}{-21}=\frac{63}{-21}\\ h=-3\end{array}$

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

– Check the solution 

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

$2\left(-4h-13\right)=37+13h$

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

$\begin{array}{c}2\left(-4\left(-3\right)-13\right)=37+13\left(-3\right)\\ 2\left(12-13\right)=37-39\\ 2\left(-1\right)=-2\\ -2=-2\end{array}$

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