Intermediate Algebra, Chapter 2, 2.1, Section 2.1, Problem 14

Solve the equation $9x + 1 = 7x - 9$, and check your solution. If applicable, tell whether the equation is an identity or contradiction.


$
\begin{equation}
\begin{aligned}

9x + 1 =& 7x - 9
&& \text{Given equation}
\\
9x - 7x =& -9 - 1
&& \text{Subtract $(7x+1)$ from each side}
\\
2x =& -10
&& \text{Combine like terms}
\\
\frac{2x}{2} =& - \frac{10}{2}
&& \text{Divide both sides by $2$}
\\
x =& -5
&&

\end{aligned}
\end{equation}
$


Checking:


$
\begin{equation}
\begin{aligned}

9(-5) + 1 =& 7 (-5) - 9
&& \text{Substitute } x = -5
\\
-45 + 1 =& -35 - 9
&& \text{Multiply}
\\
-44 =& -44
&& \text{True}

\end{aligned}
\end{equation}
$