A statement is an assertion or a sentence that is either true or false, but not both.
A variable is a symbol that may represent any member of a specified set called replacement set or domain of that variable.
A mathematical expression is a symbolic representation for a member.
An equation is a sentence that asserts that two mathematical expressions are equal.
called an inequation or an inequality. An inequation may contain one variable or more than one variable.
Some general rules of inequalities
In this section, you will learn how so solve inequalities. "Solving" an inequality means finding all of its solutions. A "solution" of an inequality is a number which when substituted for the variable makes the inequality a true statement.
Linear inequations
An inequation is said to be linear if each term of the algebraic expression (or expressions) of the inequation contains first degree variables (not the product of variables).
Graphs of linear inequations
Consider the equation x = 0, x = 1, y = 0, y = -2. i) x = 0 represents y-axis. ii) x = 1 represents line parallel to y-axis. iii) y = 0 represents x-axis. iv) y = -2 represents line parallel to x-axis.
Simultaneous inequations
Two inequalities, containing the same unknowns, are called equivalent, if they are valid at the same values of the unknowns. The same definition is used for the equivalence of two systems of simultaneous inequalities. Solving of inequalities is a process of transition from one inequality to another, equivalent inequality.
Summary
A half-plane in the x-y plane is called a closed half-plane if the points on the line separating the half-planes are also included in the half-plane.
Conclusion
Linear inequations denote a user-friendly branch of mathematics which enables us to be very comfortable with the number line and properties of numbers.
