Beginning Algebra With Applications, Chapter 3, 3.2, Section 3.2, Problem 152

Solve $4(1-3x) + 7x = 9$ and check.


$
\begin{equation}
\begin{aligned}

4(1-3x) + 7x =& 9
&& \text{Given equation}
\\
\\
4-12x + 7x =& 9
&& \text{Apply Distributive Property}
\\
\\
-12x+7x =& 9-4
&& \text{Subtract } 4
\\
\\
-5x =& 5
&& \text{Simplify}
\\
\\
\frac{\cancel{-5}x}{\cancel{-5}} =& \frac{5}{-5}
&& \text{Divide by } -5
\\
\\
x =& -1
&&
\end{aligned}
\end{equation}
$


Checking:


$
\begin{equation}
\begin{aligned}

4[1-3(-1)] + 7(-1) =& 9
&& \text{Substitute } x = -1
\\
4(4)-7 =& 9
&& \text{Simplify}
\\
16-7 =& 9
&& \text{Simplify}
\\
9 =& 9
&&

\end{aligned}
\end{equation}
$