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:


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