Chapter 2: Equations and Inequalities

Linear Equations

To solve a linear equation, we may apply the rules below. The values $a$, $b$ and $c$ are real numbers, unless otherwise stated.

1. Addition and subtraction rules:
   1. If $a=b$, then $a+c=b+c$.
   2. If $a=b$, then $a-c=b-c$.
2. Multiplication and division rules:
   1. If $a=b$, then $ca=cb$.
   2. If $a=b$, then $\displaystyle \frac{a}{c}=\frac{b}{c}$ ($c \neq 0$).
3. Switching sides:
   1. If $a=b$, then $b=a$.