Mathematical Equalities

Mathematical equalities are expressions that establish a relationship of equality between two expressions or quantities. They are fundamental in mathematics, since they allow us to perform operations and solve equations.

A mathematical equality is composed of two sides: the left side and the right side, separated by the equal sign (=). Each side of the equality can contain terms, mathematical operations and variables.

Some common examples of mathematical equalities are:

Numerical equality. States that two numerical quantities are equal. For example: 3 + 4 = 7.

Algebraic equality. Involves variables and can represent more general relationships. For example: 2x + 3 = 7.

Functional equality. Relates two functions and states that for certain values of the variable, the functions give the same result. For example: f(x) = g(x).

Trigonometric equality. Refers to an equality involving trigonometric functions, such as sine, cosine or tangent. For example: sen²(x) + cos²(x) = 1.

Vector equality. States that two vectors are equal in magnitude and direction. For example: →AB = →CD.

Solving mathematical equalities involves finding the value or values of the variables that make the equality true. This can be accomplished by algebraic techniques, manipulating the terms and applying mathematical properties and rules. In some cases, it is necessary to use numerical or graphical methods to find approximate solutions.

It is important to keep in mind that mathematical equalities must respect mathematical rules and properties, such as the reflexive, transitive and symmetric property of equality. In addition, equivalent operations can be applied on both sides of the equality without altering its validity.