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# Equation

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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 $4(3y^{99}) +76=42+3x$ 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:
$2 \cdot (x+4)=2x+8 \rightarrow \text{true}$
• 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:
$2 \cdot x=8 \rightarrow x=4$

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:

## References

1. "Compendium of Mathematical Symbols" (in en-US). 2020-03-01.
2. "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.
3. 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