Intermediate Algebra, Chapter 2, 2.1, Section 2.1, Problem 40

Solve the equation $4(x + 2) -8x - 5 = -3x + 9 - 2(x + 6)$, and check your solution. If applicable, tell whether the equation is an identity or contradiction.


$
\begin{equation}
\begin{aligned}

4(x + 2) -8x - 5 =& -3x + 9 - 2(x + 6)
&& \text{Given equation}
\\
4x + 8 - 8x - 5 =& -3x + 9 - 2x - 12
&& \text{Distributive property}
\\
-4x + 3 =& -5x - 3
&& \text{Combine like terms}
\\
-4x + 5x =& -3-3
&& \text{Add $(5x - 3)$ from each side}
\\
x =& -6
&& \text{Combine like terms}

\end{aligned}
\end{equation}
$


Checking:


$
\begin{equation}
\begin{aligned}

4(-6+2) - 8(-6)-5 =& -3(-6) + 9 - 2 (-6 + 6)
&& \text{Substitute } x = - 9
\\
4(-4) - 8(-6) - 5 =& -3(-6) + 9 - 2 (0)
&& \text{Add inside parentheses first}
\\
-16 + 48 - 5 =& 18 + 9 - 0
&& \text{Multiply}
\\
27 =& 27
&& \text{True}

\end{aligned}
\end{equation}
$