Equation

Template:For A mathematical equation is an expression containing two mathematical objects connected by an equals sign (=) . The equals sign says that both sides are exactly equal, or of the same value. An equation can be as simple as $x=0$, or as complex 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:

$2\cdot (x+4)=2x+8\to \text{true}$

• The kind of equation that is only true for certain values of the variable(s). The equation is only true if the variable(s) have that value. For example:

$2\cdot x=8\to x=4$

The second kind is often used to solve problems in which finding the value of some variables is involved. For example, if

$2x=8$, $x=\frac{8}{2}=4$

The second kind of equation is used in algebra. For example, to solve the equation $2x=8$ for $x$, one would follow an algebraic rule to find that $x=4$.

Types of equations

Equations can be classified by the types of operations and quantities involved. For example:

• 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, which include:
  • Ordinary differential equation
  • Partial differential equation

Related pages

• Equation solving
• Formula
• Rate equation
• System of linear equations

References

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