"An equation is a mathematical formula that expresses the equality of two expressions, by connecting them with the equals sign =."
Expressions and equations are the building blocks of algebra, and understanding how to work with them is crucial in solving algebraic problems.
Variables and Constants: Understanding the difference between symbols that represent unknown values (variables) and fixed values (constants).
Basic Operations: Adding, subtracting, multiplying, and dividing expressions.
Order of Operations: Knowing the correct order in which to perform operations to solve an equation.
Properties of Numbers: Understanding basic properties such as commutative, associative, and distributive.
Simplifying Equations: Combining like terms and applying other simplification rules to make expressions easier to work with.
Linear Equations: Solving equations that involve only one variable.
Quadratic Equations: Solving equations that involve variables raised to the power of two.
Inequalities: Understanding and solving equations where the solution is not a single value, but a range of values.
Systems of Equations: Solving two or more equations at the same time.
Polynomials: Understanding the basics of expressions where variables are raised to powers of three or higher.
Factorization: Rewriting expressions as a product of simpler terms.
Exponents and Roots: Understanding how to work with expressions that involve powers and roots.
Rational Expressions: Understanding expressions that involve fractions with variables in the numerator and denominator.
Word Problems: Applying algebraic concepts to real-world scenarios.
Graphing Equations: Understanding how algebraic equations can be represented visually on a graph.
Linear equations: An equation where the highest power of the unknown variable is 1.
Quadratic equations: An equation where the highest power of the unknown variable is 2.
Cubic equations: An equation where the highest power of the unknown variable is 3.
Quartic equations: An equation where the highest power of the unknown variable is 4.
Inverse equations: An equation in which the value of the unknown variable is obtained by inverting the given equation.
Polynomial equations: An equation in which the unknown variable is a polynomial function.
Radical equations: An equation containing one or more radical expressions.
Exponential equations: An equation involving exponential functions.
Logarithmic equations: An equation involving logarithmic functions.
Trigonometric equations: An equation involving trigonometric functions.
Absolute value equations: An equation in which an absolute value is involved.
Rational equations: An equation involving rational functions.
Parametric equations: A set of equations where the variables are expressed in terms of one or more parameters.
Simultaneous equations: A set of equations with more than one unknown variable.
Vector equations: An equation involving vectors.
Differential equations: An equation that relates a function to one or more of its derivatives.
Integral equations: An equation involving integrals.
Homogeneous equations: An equation where every term has the same degree.
Non-homogeneous equations: An equation where the highest degree of some of the terms is different from the rest of the terms.
Partial differential equations: An equation involving partial derivatives of a function of several variables.
Fractional equations: An equation involving fractional order calculus.
Matrix equations: An equation involving matrices.
"In French, an équation is defined as containing one or more variables."
"In English, any well-formed formula consisting of two expressions related with an equals sign is an equation."
"Solving an equation containing variables consists of determining which values of the variables make the equality true."
"The variables for which the equation has to be solved are also called unknowns."
"The values of the unknowns that satisfy the equality are called solutions of the equation."
"There are two kinds of equations: identities and conditional equations."
"An identity is true for all values of the variables."
"A conditional equation is only true for particular values of the variables."
"The "=" symbol, which appears in every equation, was invented in 1557 by Robert Recorde."
"The "=" symbol was invented in 1557 by Robert Recorde."
"Robert Recorde invented the "=" symbol."
"Robert Recorde considered that nothing could be more equal than parallel straight lines with the same length."
"The "=" symbol is used to connect two expressions in an equation to express their equality."
"The equals sign connects two expressions in an equation to indicate their equality."
"Two expressions related with an equals sign form an equation."
"The word equation and its cognates in other languages may have subtly different meanings."
"Variables in equations represent unknowns that need to be solved."
"Well-formed formulas consist of two expressions related by an equals sign in an equation."
"Solving an equation is done to find values of variables that make the equality true."