Intermediate Algebra, Chapter 2, 2.1, Section 2.1, Problem 18

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


$
\begin{equation}
\begin{aligned}

-4x + 5x - 8 + 4 =& 6x - 4
&& \text{Given equation}
\\
x - 4 =& 6x - 4
&& \text{Combine like terms}
\\
x - 6x =& -4 + 4
&& \text{Subtract $(6x-4)$ from each side}
\\
-5x =& 0
&& \text{Combine like terms}
\\
\frac{-5x}{-5} =& \frac{0}{-5}
&& \text{Divide both sides by $-5$}
\\
x =& 0
&&

\end{aligned}
\end{equation}
$


Checking:


$
\begin{equation}
\begin{aligned}

-4(0) + 5(0) - 8 + 4 =& 6(0) - 4
&& \text{Substitute } x = 0
\\
-8 + 4 =& -4
&& \text{Multiply}
\\
-4 =& -4
&& \text{True}

\end{aligned}
\end{equation}
$

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