Chapter 2.3, Problem 40P

Can you solve the equation $\frac{2}{3}(4x-5)=8$ by using the Division Property of Equality? Explain.

To determine

To Solve: the given equation.

Explanation of Solution

Given information:

  $\frac{2}{3}\left(4x-5\right)=8$

Solve by using the division property

  $\begin{array}{l}\frac{\frac{2}{3}\left(4x-5\right)}{\frac{2}{3}}=\frac{8}{\frac{2}{3}}\\ \Rightarrow 4x-5=\frac{24}{2}\\ \Rightarrow 4x-5=12\\ \Rightarrow 4x=12+5\\ \Rightarrow 4x=17\\ \Rightarrow \frac{4x}{4}=\frac{17}{4}\\ \Rightarrow x=\frac{17}{4}\\ \end{array}$