Question

Tutorial Drill: #1

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. > , < ,≥ ,≤ 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:

\(\large{3x-2<0}\)
\(\large{2x+3} \ge 0\)

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 equation as an example :

LHS of this inequation is \(\cfrac{3-2x}{5}\) and RHS is \(\cfrac{x}{3}-4\)
we observe that:

For x = 9 , We have LHS = \(\cfrac{3-2*9}{5} = -3\) and RHS : \(\cfrac{9}{3} - 4 = -1\)

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) 2x - 4 \(\le\) 0
2x - 4 + 4 \(\le\) 4
2x \(\le\) 4
x \(\le\) 2

[Properties of Linear Inequalities Info. has been taken from internet]

Answer 2

Tutorial Drill #1 is a part of my (mathslover's) tutorials that he contributed on OpenStudy. To make those available to all, I'm trying to repost them here, for the user's benefit.

Thanks!

Answer 3

Link to this tutorial on OpenStudy: http://openstudy.com/study#/updates/4ff513f9e4b01c7be8c83b1d

Answer 4

Would you like me to re-open this question for you?

Answer 5

(So you can have both tutorials open at once :))

Answer 6

Yeah, if you can! :) It would be great.

Answer 7

Gladly ^_^

Answer 8

Done :)

Answer 9

Thanks man!

Answer 10

Interesting.
*thumbs up* \(:) \)

Answer 11

Thanks, @MARC ! :)

Answer 12

^_^

Answer 13

Well done :)

Answer 14

THANK. YOU. HOLY. LORD.

Answer 15

TYYYYYYYYYYY

Answer 16

This helps a lot !