Beginning Algebra With Applications, Chapter 3, 3.2, Section 3.2, Problem 166

Solve $-4 [x - 2 (2x - 3)] + 1 = 2x-3$ and check.


$
\begin{equation}
\begin{aligned}

-4 [x - 2 (2x - 3)] + 1 =& 2x-3
&& \text{Given equation}
\\
\\
-4(x-4x + 6) + 1 =& 2x - 3
&& \text{Apply Distributive Property}
\\
\\
-4x + 16x - 24 + 1 =& 2x-3
&& \text{Apply Distributive Property}
\\
\\
-4x + 16x - 2x =& -3 + 24 -1
&& \text{Subtract $2x$ and subtract } (-24+1)
\\
\\
10x =& 20
&& \text{Simplify}
\\
\\
\frac{\cancel{10}x}{\cancel{10}} =& \frac{20}{10}
&& \text{Divide by } 10
\\
\\
x =& 2
&&


\end{aligned}
\end{equation}
$


Checking:


$
\begin{equation}
\begin{aligned}

-4 [2-2(2(2) - 3)] + 1 =& 2(2) - 3
&& \text{Substitute } x = 2
\\
-4(2-2) + 1 =& 4-3
&& \text{Simplify}
\\
1 =& 1
&&

\end{aligned}
\end{equation}
$