###### Example2.5.2

A number plus $$2$$ is $$6\text{.}$$ What is that number?

You may be so familiar with basic arithmetic that you know the answer already. The algebra approach would be to start by translating “A number plus $$2$$ is $$6$$” into a math statement — in this case, an equation:

\begin{equation*} x+2=6 \end{equation*}

where $$x$$ is the number we are trying to find. In other words, what should be substituted in for $$x$$…

\begin{equation*} x+2=6 \end{equation*}

… to make the equation true?

Now, how do you determine what $$x$$ is? One valid option is to just imagine what number you could put in place of $$x$$ that would result in a true equation. Would $$0$$ work? No, that would mean $$0+2\stackrel{\text{no}}{=}6\text{.}$$ Would $$17$$ work? No, that would mean $$17+2\stackrel{\text{no}}{=}6\text{.}$$ Would $$4$$ work? Yes, because $$4+2=6$$ is a true equation.

So one solution to $$x+2=6$$ is $$4\text{.}$$ No other numbers are going to be solutions, because when you add $$2$$ to something smaller or larger than $$4\text{,}$$ the result is going to be smaller or larger than $$6\text{.}$$

in-context