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Q9.

Expert-verified

Pre-algebra

Found in: Page 120

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.
$12 = \frac{f}{2} - 8$

The solution for the equation $12 = \frac{f}{2} - 8$ is $f = 40$ .

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 variables.

$\begin{array}{l} 12 = \frac{f}{2} - 8 \\ 12 + 8 = \frac{f}{2} \\ 20 = \frac{f}{2} \end{array}$

Step 2 – Solve for f

Multiply both sides of the equation $20 = \frac{f}{2}$ by 2 and simplify.

$\begin{array}{l} 20 \times 2 = \frac{f}{2} \times 2 \\ f = 40 \end{array}$

Therefore, the solution of the equation is $f = 40$ .

Step 3 – Check the solution

To check the solution, write the original equation and substitute the value of $f$ .

localid="1649207493077" $12 = \frac{f}{2} - 8$

Now, substitute $f = 40$ and check the result.

$12 = \frac{40}{2} - 8 12 = 20 - 8 12 = 12$

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

$\begin{array}{l} 12 = \frac{40}{2} - 8 \\ 12 = 20 - 8 \\ 12 = 12 \end{array}$

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