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# Equation

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For a chemical type of equation, see Chemical equation.

A mathematical **equation** is an expression containing two mathematical objects connected by an equals sign (=) .^{[1]}^{[2]}^{[3]}^{[4]} 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 [math]4(3y^{99}) +76=42+3x[/math] 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]2 \cdot (x+4)=2x+8 \rightarrow \text{true}[/math]

- 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:

- [math]2 \cdot x=8 \rightarrow x=4[/math]

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

- [math] 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 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:

## Related pages

## References

- ↑ "Compendium of Mathematical Symbols" (in en-US). 2020-03-01. https://mathvault.ca/hub/higher-math/math-symbols/.
- ↑ "Equations and Formulas". https://www.mathsisfun.com/algebra/equation-formula.html.
- ↑ "A statement of equality between two expressions. Equations are of two types,
**identities**and**conditional equations**(or usually simply "equations")". «*Equation*», in*Mathematics Dictionary*, Glenn James et Robert C. James (éd.), Van Nostrand, 1968, 3 ed. 1st ed. 1948, p. 131. - ↑ Une équation est une égalité entre deux expressions mathématiques, donc une formule de la forme A = B, où les deux membres A et B de l'équation sont des expressions où figurent une ou plusieurs variables, représentées par des lettres. ÉQUATION, mathématique - Encyclopædia Universalis