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Q18.

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.**

$\mathbf{14}\mathbf{a}\mathbf{-}\mathbf{93}\mathbf{=}\mathbf{49}\mathbf{-}\mathbf{57}\mathbf{a}$

The solution for the equation $14a-93=49-57a$ is $a=2$.

Write the original equation and separate the variable and constants.

$\begin{array}{c}14a-93=49-57a\\ 14a+57a-93=49-57a+57a\text{}\left(\text{add 57a to both sides}\right)\\ 71a-93=49\text{}\left(\text{simplify}\right)\\ 71a-93+93=49+93\text{}\left(\text{add 93 to both sides}\right)\\ 71a=142\text{}\left(\text{simplify}\right)\end{array}$

Now, divide both sides of the equation by 71.

$\begin{array}{c}\frac{71a}{71}=\frac{142}{71}\\ a=2\end{array}$Therefore, the solution of the equation is $a=2$.

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

$14a-93=49-57a$

Now, substitute $a=2$ and check the result.

$\begin{array}{c}14\times 2-93=49-57\times 2\\ 28-93=49-114\\ -65=-65\end{array}$As the left-hand side is equal to right hand side, this signifies that the solution is correct.

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