Suggested languages for you:

Americas

Europe

Q5

Expert-verified
Found in: Page 41

### Geometry

Book edition Student Edition
Author(s) Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen
Pages 227 pages
ISBN 9780395977279

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

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

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

$2b=24-6b$ Distributive property

$8b=24$ Addition property of equality.

$b=3$ Division property of equality

See the step by step solution

## Step 1. Apply the multiplication property of equality.

If $p=q$ then, $rp=rq$.

## Step 2. Description of step.

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

$\begin{array}{c}3×\frac{2}{3}b=3\left(8-2b\right)\\ 2b=3\left(8-2b\right)\end{array}$

## Step 3. Apply distributive property.

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

$\begin{array}{c}2b=3×8-3×\left(2b\right)\\ =24-6b\end{array}$

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

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

$8b=24$

## Step 6. Apply division property of equality.

If $p=q$ and $r\ne 0$, 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.

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

Therefore, the value of b is 3.