Introduction to Linear Inequalities
* Inequalities: Two real numbers or two algebraic expressions related by the symbols, ‘<’, ‘>’, ‘≤’ or ‘≥’, from an inequality.
* The values of x for which the statements holds true are called the solutions of the inequality.
* Equal numbers may be added to (or subtracted from) both the sides of an inequality without affecting the sign of inequality.
* Both the sides of an inequality can be multiplied (or divided) by the same positive number. However, when both sides are multiplied or divided by a negative number, then the sign of inequality is reversed.
Graphical Solution of Linear Inequalities in Two Variables
* The values of the variables for which an inequality holds true is called the solution of the inequality.
* A vertical line divides the Cartesian plane into left and right half planes.
* A non-vertical line will divide the plane into an upper half plane and a lower half plane.
Graphical Solution of a System of Linear Inequalities
* The solution set of system linear inequalities is the common solution set that satisfies every inequality in that system.