First Degree Equations

Why

Definition

Suppose $f: \R \to \R $ is a first-order polynomial. In other words, there are coefficients $\alpha , \beta \in \R $, $\alpha \neq 0$, so that $f(x) = \alpha x + \beta $ for every $x \in \R $. Then $f(x) = 0$ is a first degree equation.

We write

\[ \alpha x + \beta = 0 \]

Notice that we can divide through by $\alpha $ to obtain,

\[ x + (\beta /\alpha ) = 0 \]

Solutions

Given a real number $a \in \R $, suppose we want to find $x \in \R $ so that

\[ x + a = 0 \]

Clearly, $x = -a$ is a solution.

Future editions will include, and will likely continue to higher degree equations. ↩︎