# 02\_Equations\_and\_Inequalities

### 2.1 The Rectangular Coordinate Systems and Graphs

pass

### 2.2 Linear Equations in One Variable

* a `linear equation` is an equation of a strait line, written in one variable. It can be written in the form

$$
ax + b = 0
$$

​ where a and b are real numbers, $a \neq 0$

linear equations in one variable can be classified into three types:

*   `identity equation`: true for all values on the variable

    $3x = 2x + x$
*   `conditional equation`: true for only some values of the variable

    $$
    \begin{align*} 5x + 2 &= 3x -6 \\ 2x &= -8 \\ x &= -4 \end{align*}
    $$
*   `inconsistent equation`: is a false statement

    $5x - 15 = 5x - 20$

### 2.4 Complex Numbers

* a complex number is `the sum of a real number and an imaginary` number

a complex number is a number of the form $a + bi$, if $a = 0$ and $b \neq 0$, the complex number is called a pure imaginary number

* an imaginary number is an `even root of a negative number`

### 2.5 Quadratic Equations

`zero-product property` states:

if $a \cdot b = 0$, then a = 0 or b = 0

a `quadratic equation` is an equation containing a second-degree polynomial; e.g.

$$
ax^2 + bx + c = 0
$$

where a, b, and c are real numbers, and $a \neq 0$
