Today is our topic of discussion Application of Inequalities .
Application of Inequalities
You have learnt to solve problems using equations. Following the same procedure, you will be able to solve problems regarding inequality.
Linear Inequality with Two Variables
We have learned to draw the graph of the linear equations with two variables of the form y = mx + c (whose general form is ax + by + c = 0) (in class 8 and class 9-10). We have seen that the graph of each equation of this type is a straight line. In XY plane, co-ordinates of any point on the graph of equation ax + by + c = 0 satisfies the equation. That means the left hand side of the equation will be zero if we replace the x and y with the abscissa and ordinate respectively of that point.
On the other hand, the co-ordinates of any point outside the graph does not satisfy the equation, in other words for abscissa and ordinate of that point the value of ax + by + c is greater or less than zero. When x and y of the expression ax + by + c are replaced respectively by the abscissa and ordinate of any point P on the plane, the value of the expression is called the value of expression at the point P and that value is generally denoted by f(P) If P is on the graph, f(P) = 0 if the point lies outside the graph then f(P) > 0 or f(P) < 0 .
As a matter of fact, in reality all points outside the graph is divided into two half-planes by the graph. For each point P of one half plane, f(P) > 0 for each point P of other half plane, f(P) < 0 In fact, for each point P on the graph, f(P) = 0 .
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