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Answers without the blur. Sign up and see all textbooks for free! Q12.

Expert-verified Found in: Page 133 ### Pre-algebra

Book edition Common Core Edition
Author(s) Ron Larson, Laurie Boswell, Timothy D. Kanold, Lee Stiff
Pages 183 pages
ISBN 9780547587776 # Solve the equation. Check your solution.$\mathbf{-}\mathbf{5}\mathbf{k}\mathbf{-}\mathbf{19}\mathbf{=}\mathbf{5}\mathbf{-}\mathbf{13}\mathbf{k}$

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

See the step by step solution

## Step 1 – Separate the variable and constants

Write the original equation and separate the variable and constants.

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

## Step 2 – 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 $k=3$.

## Step 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.

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

As the left-hand side is equal to right hand side, this signifies that the solution is correct. ### Want to see more solutions like these? 