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 ${\displaystyle x=0}$, or as complex as ${\displaystyle 4(3y^{99})+76=42+3x}$ 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:

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

• 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:

${\displaystyle 2\cdot x=8\rightarrow x=4}$

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

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

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

1. ↑ "Compendium of Mathematical Symbols". Math Vault. 2020-03-01. Retrieved 2020-09-01.
2. ↑ "Equations and Formulas". www.mathisfun.com. Retrieved 2020-09-01.
3. ↑ "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.
4. ↑ 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