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}
$