Question

Solve the equation. Check your solution.

$\mathbf{-}\mathbf{5}\mathbf{k}\mathbf{-}\mathbf{19}\mathbf{=}\mathbf{5}\mathbf{-}\mathbf{13}\mathbf{k}$

Short answer

The solution for the equation $-5k-19=5-13k$ is $k=3$.

Step-by-step solution

– Separate the variable and constants

Write the original equation and separate the variable and constants.

$\begin{array}{c}-5k-19=5-13k\\ -5k-19+19=5-13k+19\left(\text{Add19tobothsides}\right)\\ -5k-0=24-13k\left(\text{Simplify}\right)\\ -5k+13k=24-13k+13k\left(\text{Add13ktobothsides}\right)\\ 8k=24\left(\text{Simplify}\right)\end{array}$

– Solve for k

Now, divide both sides of the equation by 8.

$\begin{array}{c}\frac{8k}{8}=\frac{24}{8}\\ k=3\end{array}$

Therefore, the solution of the equation is $k=3$.

– Check the solution 

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

$-5k-19=5-13k$

Now, substitute $k=3$ and check the result.

$\begin{array}{c}-5\times 3-19=5-13\times 3\\ -15-19=5-39\\ -34=-34\end{array}$

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