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Section 2.4 Closing Ideas

Most textbooks will have hundreds of problems for you to work on, especially for a section like this one. And there's certainly value to practicing those manipulations over and over again so that you can get a lot of experience. However, the approach of this textbook is much more about slowing you down to help you create a solid mental framework for understanding mathematical ideas.

One piece of that framework of mathematical thinking is the ability to take something complicated and break it down into simpler pieces. One of the ways that manifests is the transition from working with numbers to working with variables. We tried to set you up with this idea in the forward direction by giving you a series of equations with numbers before asking you to work with variables:

\begin{equation*} \left. \begin{aligned} x + 3 \amp = 7 \longrightarrow \text{Subtract $3$ from both sides} \\ x + 4 \amp = 7 \longrightarrow \text{Subtract $4$ from both sides} \\ x + 5 \amp = 7 \longrightarrow \text{Subtract $5$ from both sides} \\ x + 6 \amp = 7 \longrightarrow \text{Subtract $6$ from both sides} \end{aligned} \right\} \implies x + b = 7 \longrightarrow \text{Subtract $b$ from both sides} \end{equation*}