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Q18.

Expert-verified

Pre-algebra

Found in: Page 133

Book edition Common Core Edition

Author(s) Ron Larson, Laurie Boswell, Timothy D. Kanold, Lee Stiff

Pages 183 pages

ISBN 9780547587776

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Short Answer

Solve the equation. Check your solution.
$14 a - 93 = 49 - 57 a$

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

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1 – Separate the variable and constants

Write the original equation and separate the variable and constants.

$\begin{matrix} 14 a - 93 = 49 - 57 a \\ 14 a + 57 a - 93 = 49 - 57 a + 57 a (add 57a to both sides) \\ 71 a - 93 = 49 (simplify) \\ 71 a - 93 + 93 = 49 + 93 (add 93 to both sides) \\ 71 a = 142 (simplify) \end{matrix}$

Step 2 – Solve for a

Now, divide both sides of the equation by 71.

\begin{matrix} \frac{71 a}{71} = \frac{142}{71} \\ a = 2 \end{matrix}

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.

$14 a - 93 = 49 - 57 a$

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

\begin{matrix} 14 \times 2 - 93 = 49 - 57 \times 2 \\ 28 - 93 = 49 - 114 \\ - 65 = - 65 \end{matrix}

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

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