Intermediate Algebra, Chapter 2, 2.1, Section 2.1, Problem 16

Solve the equation $2x + 4 - x = 4x - 5$, and check your solution. If applicable, tell whether the equation is an identity or contradiction.


$
\begin{equation}
\begin{aligned}

2x + 4 - x =& 4x - 5
&& \text{Given equation}
\\
x + 4 =& 4x - 5
&& \text{Combine like terms}
\\
x - 4x =& -5-4
&& \text{Subtract $(4x+4)$ from each side}
\\
-3x =& -9
&& \text{Combine like terms}
\\
\frac{-3x}{-3} =& \frac{-9}{-3}
&& \text{Divide both sides by $-3$}
\\
x =& 3
&&

\end{aligned}
\end{equation}
$


Checking:


$
\begin{equation}
\begin{aligned}

2(3) + 4 - 3 =& 4(3) - 5
&& \text{Substitute } x = 3
\\
6 + 4 - 3 =& 12 - 5
&& \text{Multiply}
\\
7 =& 7
&& \text{True}

\end{aligned}
\end{equation}
$