Intermediate Algebra, Chapter 2, 2.1, Section 2.1, Problem 20

Solve the equation $2(3-2x) = x - 4$, and check your solution. If applicable, tell whether the equation is an identity or contradiction.


$
\begin{equation}
\begin{aligned}

2(3-2x) =& x - 4
&& \text{Given equation}
\\
6-4x =& x - 4
&& \text{Distributive property}
\\
-4x - x =& -4-6
&& \text{Subtract $(x+6)$ from each side}
\\
-5x =& -10
&& \text{Combine like terms}
\\
\frac{-5x}{-5} =& \frac{-10}{-5}
&& \text{Divide both sides by $-5$}
\\
x =& 2
&&

\end{aligned}
\end{equation}
$


Checking:


$
\begin{equation}
\begin{aligned}

2[3-2(2)] =& 2-4
&& \text{Substitute } x = 2
\\
2(3-4) =& 2-4
&& \text{Multiply}
\\
2(-1) =& 2-4
&& \text{Subtract inside the parentheses}
\\
-2 =& -2
&& \text{True}

\end{aligned}
\end{equation}
$