"In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions."
Inequalities involve comparing two expressions or values to determine whether they are less than, greater than, or equal to each other.
Solving linear inequalities: Solving inequalities with one variable using addition, subtraction, multiplication, and division.
Graphing linear inequalities: Plotting inequalities on a number line and the coordinate plane.
Compound inequalities: Two or more inequalities joined with either an "and" or "or" forming a compound inequality.
Absolute value inequalities: Inequalities involving absolute values and how to solve them.
Word problems with inequalities: Systems of inequalities, optimization problems and other real-world applications.
Rational inequalities: Inequalities involving fractions and how to solve.
Exponential and logarithmic inequalities: Inequalities involving exponents and logarithmic functions.
Quadratic inequalities: Inequalities involving quadratic functions and how to solve.
Polynomial inequalities: Inequalities involving polynomials and how to solve.
Systems of inequalities: Solving systems of linear and nonlinear inequalities.
Interval notation: Representing solutions of inequalities on a number line using interval notation.
Inequalities with absolute value functions: Inequalities involving absolute value functions.
Inequalities with piecewise functions: Inequalities involving piecewise functions.
Inequalities in higher dimensions: Inequalities involving two or more variables and how to graph them.
Linear Inequality: An inequality whose highest power of an unknown quantity is limited to 1.
Quadratic Inequality: An inequality whose highest power of an unknown quantity is limited to 2.
Rational Inequality: An inequality involving a rational function, i.e., a function comprising a quotient of two polynomial functions.
Absolute Value Inequality: An inequality whose unknown quantity is enclosed within absolute value bars.
Exponential Inequality: An inequality involving exponential functions with unknown quantity in the exponent.
Logarithmic Inequality: An inequality involving logarithmic functions with unknown quantity.
Trigonometric Inequality: An inequality involving trigonometric functions such as sine, cosine, tangent, etc.
Polynomial Inequality: An inequality involving polynomial functions of higher degree.
Radical Inequality: An inequality involving a radical function, i.e., a function comprising a root.
System of Linear Inequalities: A system comprising of multiple linear inequalities involving the same variables.
System of Non-Linear Inequalities: A system comprising of multiple non-linear inequalities involving the same variables.
"It is used most often to compare two numbers on the number line by their size."
"The notation a < b means that a is less than b."
"The notation a > b means that a is greater than b."
"These relations are known as strict inequalities, meaning that a is strictly less than or strictly greater than b. Equivalence is excluded."
"The notation a ≤ b or a ⩽ b means that a is less than or equal to b (or, equivalently, at most b, or not greater than b)."
"The notation a ≥ b or a ⩾ b means that a is greater than or equal to b (or, equivalently, at least b, or not less than b)."
"The relation not greater than can also be represented by a ≯ b, the symbol for 'greater than' bisected by a slash, 'not'."
"The same is true for not less than and a ≮ b."
"The notation a ≠ b means that a is not equal to b; this inequation sometimes is considered a form of strict inequality."
"The notation a ≪ b means that a is much less than b."
"The notation a ≫ b means that a is much greater than b."
"In all of the cases above, any two symbols mirroring each other are symmetrical; a < b and b > a are equivalent, etc."
"In engineering sciences, less formal use of the notation is to state that one quantity is 'much greater' than another, normally by several orders of magnitude."
"The notation a < b means that a is less than b."
"The notation a ≥ b means that a is greater than or equal to b."
"Equivalence is excluded."
"The relation not greater than can also be represented by a ≯ b, the symbol for 'greater than' bisected by a slash, 'not'."
"It does not say that one is greater than the other; it does not even require a and b to be members of an ordered set."
"This implies that the lesser value can be neglected with little effect on the accuracy of an approximation."