Kerala State Board New Syllabus Plus One Maths Notes Chapter 6 Linear Inequalities.
Kerala Plus One Maths Notes Chapter 6 Linear Inequalities
Two real numbers or two algebraic expressions related by the symbols <, >, ≤ or ≥ form an inequality. In this unit we study linear inequalities in one and two variables, their formation and solution graphically.
Solve inequality calculator or quadratic inequalities with our free step-by-step algebra calculator.
I. Linear Inequalities in One Variable
The solution of an inequality in one variable is a value of the variable ‘x’ which makes it a true statement.
Equal numbers can be added or subtracted from both sides of the inequation.
If we multiply or divide both sides of an inequation by a positive number, the inequality sign will not be changed.
If we multiply or divide both sides of an inequation by a negative number, the inequality sign will be reversed.
To represent x < a (or x > a) on a number line, put a circle on the number ‘a’ and a dark line to the left (or right) of the number ‘a’.
To represent x ≤ a (or x ≥ a) on a number line, put a dark circle on the number ‘a’ and a dark line to the left (or right) of the number ‘a’.
II. Linear Inequalities in two Variables
The region containing all the solutions of an inequality is called the solution region.
In order to identify the half-plane represented by inequality, it is just sufficient to take any point (a, b) [say point (0, 0)] not on the line and check whether it satisfies the inequality or not. If it satisfies, then the inequality represents the half-plane and shade the region which contains the point, otherwise, the inequality represents that half-plane which does not contain the point within it.
If the inequality is of the type ax + by ≥ c or ax + by ≤ c, then the point on the line ax + by = c is also included in the solution. So draw a dark line in the solution region.
If the inequality is of the type ax + by > c or ax + by < c, then the point on the line ax + by = c are not to be included in the solution. So draw a broken or dotted line in the solution region.