Chapter 2: Q5 (page 41)

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

Short Answer

Expert verified

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

Step by step solution

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

Short Answer

Step by step solution

Step 1. Apply the multiplication property of equality.

Step 2. Description of step.

Step 3. Apply distributive property.

Step 4. Apply the addition property of equality.

Step 5. Description of step.

Step 6. Apply division property of equality.

Step 7. Description of step.

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Justify each step.23b=8−2b2b=38−2b2b=24−6b8b=24b=3

Short Answer

Step by step solution

Step 1. Apply the multiplication property of equality.

Step 2. Description of step.

Step 3. Apply distributive property.

Step 4. Apply the addition property of equality.

Step 5. Description of step.

Step 6. Apply division property of equality.

Step 7. Description of step.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Logic and Functions

Theoretical and Mathematical Physics

Calculus

Statistics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

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