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.

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