Equation

Template:For A mathematical equation is an expression containing at least one variable (=unknown value) and an "equals sign" ( = ) with a mathematical expression on each side of it. The equals sign says that both sides are exactly the same value. An equation can be as simple as x=0, or as hard as 4(3y^99)+76=42÷3x or harder.

There are two kinds of mathematical equations:

• The kind of equation that is either true or false; these are also called identities. For example:

[math]\displaystyle{ 2 \cdot (x+4)=2x+8 \rightarrow true }[/math]

• The kind of equation that lets you calculate the value of one or several variables. The equation is only true if the variable(s) have that value. For example:

[math]\displaystyle{ 2 \cdot x=8 \rightarrow x=4 }[/math]

The second kind is often used to solve problems in which you have to know the value of some variables. For example,

[math]\displaystyle{ \text{if}\, 2x = 8, \, x = \frac{8}{2} = 4. }[/math]

The second kind of equation is used in algebra. For example, to solve the equation 2x = 8 by finding x you would follow an algebraic rule. Then you can work out that x = 4.

Types of equations

Equations can be classified by the types of operations and quantities involved. Some types of equations are:

• An algebraic equation is an equation in which both sides are polynomials. These are further classified by degree:
  • linear equation for degree one
  • quadratic equation for degree two
  • cubic equation for degree three
  • quartic equation for degree four
  • quintic equation for degree five
• A Diophantine equation is an equation where the unknowns are required to be integers
• A differential equation is a functional equation involving derivatives of the unknown functions

Related pages

• Formula

References

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