Linear Inequalities of 10th Standard
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In 10th standard syllabus, graphing is important factor and easily can be done by following some predefined steps. But when this application is used for linear inequalities then it gets complex. Because although linear inequalities are linear form mathematical expressions but still its answer is not a fixed value, it stays in a certain limit of integer range.
This integer range is decided according to the inequality relation and the numerical integer value of the linear inequalities equation. Inequality is introduced in any equation by using the comparison operators which are “less than(<) or greater than(>) “ and “ greater than equal to(>=) or less than(<=) equal to”.
The representation of any linear inequality equation is same as any linear equation by just replacing the equality relation with inequality as:
x + y =1 ( linear equation form )
x + y <1 ( linear inequality form )
To simplify expressions of linear inequalities, two standard principles are used which are addition principle and multiplication principle:
According to Addition principle ‘ if ‘p’ is less than ‘q’ then (p+c) will also be less than (q+ c) : if p and by multiplication principle: if p
0 than pc< qc
and if c<0 than pc > qc.
Student gets introduced with linear inequalities in their previous standards but in 10th these problems are more complex, for example : x2 + 3y2 > 18 and x + y2 > 9
The above equation is compound inequality which is joined with disjunction. But the tough part of it is that the equations are not in linear form so you have to convert them first into linear form to apply the standard principles on it.
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