# Equations

### Equality

An **equality** is composed of two algebraic expressions united by the equal sign.

2x + 3 = 5x − 2

An** equality** can be:

**False: **

2x + 1 = 2 · (x + 1)

2x + 1 = 2x + 2 1≠2.

**True **

2x + 2 = 2 · (x + 1)

2x + 2 = 2x + 2 2 = 2

### Identity

**An identity is an equality that is true for any value of the letters or variables.**

2x + 2 = 2 · (x + 1) 2x + 2 = 2x + 2 2 = 2

### Equation

**An equation is an equality that is true for some values of the letters or variables. **

x + 1 = 2 x = 1

The** members** of an equation are** each of the expressions that appear on both sides of the equal sign. **

The **terms** are the addends within the members.

The **unknowns** are the letters that appear in the equation.

The **solutions** or **roots** are the values that the letters must take to make the equality is true.

2x − 3 = 3x + 2 x = 5

2 · (5) − 3 = 3 · (5) + 2

− 10 −3 = −15 + 2 −13 = −13

The** degree** of an equation is the largest of the degrees of the monomials that its members form.

### Types of Equations According to their Degree

5x + 3 = 2x +1 **Linear equation**.

5x + 3 = 2x^{2} + x ** Quadratic equation. **

5x^{3} + 3 = 2x + x^{2}^{} ** Cubic equation**.

5x^{3} + 3 = 2x^{4} +1 **Quartic Equation.**