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.

Terms of an Equation

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 = 2x2 + x            Quadratic equation.

5x3 + 3 = 2x + x2             Cubic equation.

5x3 + 3 = 2x4 +1             Quartic Equation.