Linear Inequalities
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Linear Inequalities
Friends! Today we are going to discuss some complex mathematical problems of
class 10th and also elaborate the solution of those problems. Most of the students
require a perfect tutor for math who would assist them whenever they get fixed in any
math problem.
Because if the doubt doesn't get cleared at the time of problem solving then those
doubts won't enable him to understand the other facts and situation of the problems.
Because we all know that in math a single problem can be asked in several ways and
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In 10th standard syl abus, 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 stil 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) wil also be less than (q+ c) : if
p<q : (p+c)<(q+ c).
and by multiplication principle: if p<q and c>0 than pc< qc
and if c<0 than pc > qc.
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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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