Beginning Algebra With Applications, Chapter 3, 3.2, Section 3.2, Problem 160

Solve $7-(5-8x) = 4x + 3$ and check.


$
\begin{equation}
\begin{aligned}

7-(5-8x) =& 4x + 3
&& \text{Given equation}
\\
\\
7-5x + 8x =& 4x+3
&& \text{Apply Distributive Property}
\\
\\
8x-4x =& 3-7 +5
&& \text{Subtract $4x$ and subtract $(7-5)$}
\\
\\
4x =& 1
&& \text{Simplify}
\\
\\
\frac{\cancel{-4}x}{\cancel{-4}} =& \frac{1}{4}
&& \text{Divide by } 4
\\
\\
x =& \frac{1}{4}
&&


\end{aligned}
\end{equation}
$


Checking:


$
\begin{equation}
\begin{aligned}

7 - \left[ 5 - 8 \left( \frac{1}{4} \right) \right] =& 4 \left( \frac{1}{4} \right) + 3
&& \text{Substitute } x = \frac{1}{4}
\\
7-(5-2) =& 1 + 3
&& \text{Simplify}
\\
4 =& 4
&&

\end{aligned}
\end{equation}
$