Intermediate Algebra, Chapter 2, 2.3, Section 2.3, Problem 18

Use the variable $x$ for the unknown, and write an equation representing the verbal sentence "if the quotient of a number and $6$ is added to twice the number, the result is $8$ less than the number". Find the number and solve the problem.

The equation is


$
\begin{equation}
\begin{aligned}

\frac{x}{6} + 2x =& x - 8
&&
\\
\\
6 \left( \frac{x}{6} + 2x \right) =& 6(x - 8)
&& \text{Multiply each side by $6$}
\\
\\
x + 12x =& 6x - 48
&& \text{Distributive property}
\\
\\
13x =& 6x - 48
&& \text{Combine like terms}
\\
\\
13x - 6x =& -48
&& \text{Subtract each side by $6x$}
\\
\\
7x =& -48
&& \text{Divide each side by $7$}
\\
\\
x =& \frac{-48}{7}
&&

\end{aligned}
\end{equation}
$