Intermediate Algebra, Chapter 2, 2.1, Section 2.1, Problem 26

Solve the equation $4(x - 9) = 8(x + 3)$, and check your solution. If applicable, tell whether the equation is an identity or contradiction.


$
\begin{equation}
\begin{aligned}

4(x - 9) =& 8(x + 3)
&& \text{Given equation}
\\
4x - 36 =& 8x + 24
&& \text{Distributive property}
\\
4x - 8x =& 24 + 36
&& \text{Subtract $(8x - 36)$ from each side}
\\
-4x =& 60
&& \text{Combine like terms}
\\
\frac{-4x}{-4} =& \frac{60}{-4}
&& \text{Divide both sides by $-4$}
\\
x =& -15
&&

\end{aligned}
\end{equation}
$


Checking:


$
\begin{equation}
\begin{aligned}

4 (-15-9) =& 8(-15 + 3)
&& \text{Substitute } x = -15
\\
4(-24) =& 8(-12)
&& \text{Work inside parentheses first}
\\
-96 =& -96
&& \text{True}

\end{aligned}
\end{equation}
$