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Answers without the blur. Sign up and see all textbooks for free! Q18.

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

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

See the step by step solution

## Step 1 – Separate the variable and constants

Write the original equation and separate the variable and constants.

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

## Step 2 – Solve for a

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 $a=2$.

## Step 3 – Check the solution

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.

$\begin{array}{c}14×2-93=49-57×2\\ 28-93=49-114\\ -65=-65\end{array}$

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