Beginning Algebra With Applications, Chapter 2, 2.3, Section 2.3, Problem 98

Translate the phrase "seven increased by a number added to twice the difference between the number and two" into a variable expression. Then simplify the expression.

$
\begin{equation}
\begin{aligned}
& \text{The unknown number: } n && \text{Assign a variable to one of the number quantities}\\
\\
& \text{Seven increased by the number: } 7 + n && \text{Use the assigned variable to write an expression for any other unknown quantity.}\\
\\
& \text{The difference between the number and two: } n - 2 \\
\\
& \text{Twice the difference between the number and two: } 2(n - 2)\\
\\
&= (7 + n) + 2(n - 2) && \text{Use the assigned variable to write the variable expression.}\\
\\
&= 7 + n + 2 (n) - 2(2) && \text{Apply Distributive Property}\\
\\
&= 7 + n + 2n - 4 && \text{Combine like terms}\\
\\
&= 3 + 3n && \text{Simplify}
\end{aligned}
\end{equation}
$