###### Example 2.5.2

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:

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

… 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 \(6\text{.}\)