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Solving Inequalities

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									                             Solving Inequalities
Solving Inequalities

The expression that is not having the equal sign but the symbol of less than or greater than in
is defined as an inequality. When finding the solution of the inequalities give the number of
variables in the given expression that defines the inequality true statement.

Basic difference in Solving Inequalities and linear equations occurs in case of dividing or
multiplying the inequality but in other cases it is very much similar as solving the linear
equation.

Sometimes equal to sign is also defined with the less than or greater than sign and called as
less than equal to or greater than equal to. There are variables and the constant values in the
expression of inequality. The symbols of inequalities are defined as :

< ( less than )

> ( greater than )

< = ( less than equal to )

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> = ( greater than equal to )

There are some examples of inequalities as :

2 ( r –1 ) >3 ( 2r +3 )

u+3<2

4x+6<=3x–5

(z+3)/2>=2/3

Solving Inequalities by using some rules :

Rule ( I ) : addition or subtraction are done the both side of the expression .

Example : p – 2 > 5 ; add 2 on both side of expression

p–2+2>5+2

or p > 7 ( solution ).

Rule ( 2 ) : when switching sides, inverse the operation .

Example : 5 – t > 4

At the time of moving from right to left side or vice versa sign of inequality > is changed to < or
vice versa 4 < 5 – t .

Rule ( 3 ) : At the time of talking about the inequality it will apply all the rules of equations but
in case of division or multiply by a positive or negative number it follows some other rules of
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inequalities . Multiplication or division operations will be done also on both side of inequality.
.It will be understand by an example as an inequality

3 < 4 is multiplied by - 5 then it gives

3*-5>4*-5

- 15 > - 20 means in solving the inequality or finding the values of the variable the solution
belongs to an interval of real numbers .

If operation is done with negative number then operations will be done on both side with the
same negative number.

Example : 2 z < + 6 ,

Then according to the rule 2 z / 2 <= + 6 / 2

z<=+3.

Example of inequalities that uses all the rules at one time :

Example : 2 k + 5 < 7

( subtract 5 from both side )

2k+5–5<7–5

2k<2

( divide both side of terms )

2k/2<2/2



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