Question

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

Answer 1

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

Answer 2

Good job !

Answer 3

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

Answer 4

U wrote it ?

Answer 5

yes i wrote that all :)

Answer 6

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

Answer 7

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

Answer 8

it is

Answer 9

a = b is an inequation?

Answer 10

oh 1 sorry i meant above equation :)

Answer 11

sorry, not trying to be that dude:)

Answer 12

@mathslover :Are You a boy ?

Answer 13

yes i am a boy ..

Answer 14

aha,no wonder!

Answer 15

Eyad, are you not a boy?

Answer 16

BEST

Answer 17

@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!

Answer 18

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