Intermediate Algebra, Chapter 2, 2.1, Section 2.1, Problem 24

Solve the equation $-6x + 2x - 11 = -2(2x - 3) + 4$, and check your solution. If applicable, tell whether the equation is an identity or contradiction.


$
\begin{equation}
\begin{aligned}

-6x + 2x - 11 =& -2(2x - 3) + 4
&& \text{Given equation}
\\
-6x + 2x - 11 =& -4x + 6 + 4
&& \text{Distributive property}
\\
-4x - 11 =& -4x + 10
&& \text{Combine like terms}
\\
-4x + 4x =& 10 + 11
&& \text{Add $(4x+11)$ from each side}
\\
0 =& 21
&& \text{False}

\end{aligned}
\end{equation}
$


Since the result, $0 = 21$, is false, the equation has no solution. So the equation $-6x + 2x - 11 = -2(2x - 3)+4$ is a contradiction.