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Q12.

Expert-verifiedFound in: Page 133

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 $k=3$.

Write the original equation and separate the variable and constants.

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

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 $k=3$.

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.

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