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Q5

Expert-verified

Geometry

Found in: Page 41

Book edition Student Edition

Author(s) Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

Pages 227 pages

ISBN 9780395977279

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Short Answer

Justify each step.
$\frac{2}{3} b = 8 - 2 b$
$2 b = 3 (8 - 2 b)$
$2 b = 24 - 6 b$
$8 b = 24$
$b = 3$

$\frac{2}{3} b = 8 - 2 b$ Given

$2 b = 3 (8 - 2 b)$ Multiplication property of equality

$2 b = 24 - 6 b$ Distributive property

$8 b = 24$ Addition property of equality.

$b = 3$ Division property of equality

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Apply the multiplication property of equality.

If $p = q$ then, $r p = r q$ .

Step 2. Description of step.

Multiply each side of the $\frac{2}{3} b = 8 - 2 b$ by 3 and simplify.

$\begin{matrix} 3 \times \frac{2}{3} b = 3 (8 - 2 b) \\ 2 b = 3 (8 - 2 b) \end{matrix}$

Step 3. Apply distributive property.

Expand the right-hand side of the equation obtained in step 2 using the distributive property.

$\begin{matrix} 2 b = 3 \times 8 - 3 \times (2 b) \\ = 24 - 6 b \end{matrix}$

Step 4. Apply the addition property of equality.

If $p = q$ and $r = s$ , then $p + r = q + s$ .

Step 5. Description of step.

Add $6 b$ on each side of $2 b = 24 - 6 b$ and simplify.

$2 b + 6 b = 24 - 6 b + 6 b$

$8 b = 24$

Step 6. Apply division property of equality.

If $p = q$ and $r \neq 0$ , then $\frac{p}{r} = \frac{q}{r}$ .

Step 7. Description of step.

Divide each side of the equation obtained in steps 5 by 8 to find the value of b.

$\begin{matrix} \frac{8 b}{8} = \frac{24}{8} \\ b = 3 \end{matrix}$

Therefore, the value of b is 3.

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