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Mathematics 19 Online
mathslover (mathslover):

So here i go with my next tutorial regarding : Linear inequalities .

mathslover (mathslover):

LINEAR INEQUATIONS : I have seen many people getting confused in this topic : Linear inequations : Inequations : A statement involving variable(s) and the sign of inequality viz. > , < ,\(\ge\) ,\(\le\) is called an inequality or an inequation An equation can be linear, cubic , qudratic etc. and it may contain 1 or more than 1 variables. for example: \(\large{3x-2<0}\) \(\large{2x+3\ge 0}\) \(\large{2x^2+y+3>3}\) Solutions of an inequation : A solution of an inequation is the value (s)of the variable (s) that makes it a true statement . \[\large{\frac{3-2x}{5}=\frac{x}{3}-4}\] Let us take the above inequation as an example : LHS of this inequation is \(\large{\frac{3-2x}{5}}\) and RHS is \(\large{\frac{x}{3}-4}\) we observe that : For x = 9 , We have LHS =\(\large{\frac{3-2*9}{5}=-3}\) and RHS =\(\large{\frac{9}{3}-4=-1}\) Clearly : -3<-1 LHS < RHS which is true. Hence x = 9 is one of the solution of this inequation. Similarly we can verify that no. greater than 7 is a solution of the given inequation. Solving a linear inequation : Properties of inequalities Let a, b and c be real numbers. Transitive Property If a < b and b < c then a < c Addition Property If a < b then a + c < b + c Subtraction Property If a < b then a - c < b - c Multiplication Property If a < b and c is positive then c*a < c*b If a < b and c is negative c*a > c*b Note: If each inequality sign is reversed in the above properties, we obtain similar properties. If the inequality sign < is replaced by <= ( less than or equal) or the sign > is replaced by >= ( greater than or equal ), we also obtain similar properties. Examplex : 1 1) \(\large{2x-4\le 0}\) \[\large{2x-4+4\le 0+4}\] \[\large{2x\le 4}\] \[\large{\frac{2x}{2}\le\frac{4}{2}}\] \[\large{x\le 2}\] 2) \(\large{2x+7\ge3}\) \[\large{2x+7-7\ge3-7}\] \[\large{2x\le-4}\] \[\large{\frac{2x}{2}\le\frac{-4}{2}}\] \[\large{x\le-2}\] some more problems regarding solving double inequality will be posted soon

OpenStudy (anonymous):

Good job !

mathslover (mathslover):

@lgbasallote , @dpaInc ,@eashmore , @waterineyes please have a look @Limitless

OpenStudy (anonymous):

U wrote it ?

mathslover (mathslover):

yes i wrote that all :)

OpenStudy (zzr0ck3r):

"Let us take the above inequation as an example " its not an inequation is it?

mathslover (mathslover):

only some help regarding properties was taken from the site analyzemath ..

mathslover (mathslover):

it is

OpenStudy (zzr0ck3r):

a = b is an inequation?

mathslover (mathslover):

oh 1 sorry i meant above equation :)

OpenStudy (zzr0ck3r):

sorry, not trying to be that dude:)

OpenStudy (anonymous):

@mathslover :Are You a boy ?

mathslover (mathslover):

yes i am a boy ..

OpenStudy (anonymous):

aha,no wonder!

OpenStudy (zzr0ck3r):

Eyad, are you not a boy?

OpenStudy (goformit100):

BEST

mathslover (mathslover):

@eyad i request u to stay on the topic ..and chat is good for letting u know about the gender of each people here . thanks!

mathslover (mathslover):

http://openstudy.com/study#/updates/4ff461cfe4b01c7be8c7b1ea just like this one .. no irrelevant replies were there. thanks!

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