Beginning Algebra With Applications, Chapter 3, 3.2, Section 3.2, Problem 162

Solve $5 [2-(2x-4)] = 2(5-3x)$ and check.


$\begin{equation} \begin{aligned} 5 [2-(2x-4)] =& 2(5-3x) && \text{Given equation} \\ \\ 5(2-2x+4) =& 10-6x && \text{Apply Distributive Property} \\ \\ 10 - 10x + 20 =& 10-6x && \text{Apply Distributive Property} \\ \\ 10-10 + 20 =& -6x+10x && \text{Add $10x$ and subtract } 10 \\ \\ 20 =& 4x && \text{Simplify} \\ \\ \frac{20}{4} =& \frac{\cancel{4}x}{\cancel{4}} && \text{Divide by } 4 \\ \\ 5 =& x && \end{aligned} \end{equation}$


Checking:


$\begin{equation} \begin{aligned} 5[2-(2(5)-4)] =& 2 [5-3(5)] && \text{Substitute } x = 5 \\ 5(2-6) =& 2(-10) && \text{Simplify} \\ -20 =& -20 && \end{aligned} \end{equation}$