Chapter 2.2, Problem 5WE

To determine

To justify: The given steps for b.

Explanation of Solution

Given:

The given steps are:

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

The justification of above steps is:

Initial given step is,

  $\frac{2}{3}b=8-2b$

Using multiplication property, multiply both sides by 3 and simplify

  $\begin{array}{l}3\times \frac{2}{3}b=3\times \left(8-2b\right)\\ \Rightarrow 2b=3\left(8-2b\right)\end{array}$

Using distributive property,

  $2b=24-6b$

Using addition property, add $6b$ on both sides and simplify

  $\begin{array}{l}2b+6b=24-6b+6b\\ \Rightarrow 8b=24\end{array}$

Using division property, divide both sides by 8 and simplify

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

Hence, the given steps are justified.