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Linear Inequation

The document explains linear inequations in one variable, defining their forms and providing rules for solving them algebraically. It outlines how to manipulate terms and the effects on the inequation sign when terms are transferred, multiplied, or divided. Additionally, it notes that solutions are expressed as solution or replacement sets and can be plotted on a number line.

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jaisiddharth17
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23 views1 page

Linear Inequation

The document explains linear inequations in one variable, defining their forms and providing rules for solving them algebraically. It outlines how to manipulate terms and the effects on the inequation sign when terms are transferred, multiplied, or divided. Additionally, it notes that solutions are expressed as solution or replacement sets and can be plotted on a number line.

Uploaded by

jaisiddharth17
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Linear inequations

LINEAR INEQUATIONS IN ONE VARIABLE :

If a,b and c are real numbers, then each of the following is called Linear Inequation in one
variable.
 𝑎𝑥 + 𝑏 > 𝑐, ==> 𝑎𝑥 + 𝑏 is greater than 𝑐
 𝑎𝑥 + 𝑏 < 𝑐, ==> 𝑎𝑥 + 𝑏 is less than 𝑐
 𝑎𝑥 + 𝑏 ≥ 𝑐, ==> 𝑎𝑥 + 𝑏 is greater than or equal to 𝑐
 𝑎𝑥 + 𝑏 ≤ 𝑐, ==> 𝑎𝑥 + 𝑏 is less than or equal to 𝑐

RULES ON SOLVING A LINEAR INEQUATION ALGEBRAICALLY :

1) On transferring a positive term from one side of an inequation to its other side, the sign of the
term becomes negative also the inequation sign remains unchanged.
Example : 3𝑥 + 4 > 5 ==> 3𝑥 > 5 − 4

2) On transferring a negative term from one side of an inequation to its other side, the sign of the
term becomes positive also the inequation sign remains unchanged.
Example : 3𝑥 − 4 > 5 ==> 3𝑥 > 5 + 4

3) If each term of an inequation is multiplied or divided by the same positive number then the
inequation sign remains unchanged.
3𝑥+4 5
Example : 3𝑥 − 4 > 5 ==> 15𝑥 − 20 > 25 , 3𝑥 + 4 > 5 ==> >5
5

4) If each term of an inequation is multiplied or divided by the same negative number then the
inequation sign will be reversed.
3𝑥+4 5
Example : 3𝑥 − 4 > 5 ==> −15𝑥 + 20 < −25 , 3𝑥 + 4 > 5 ==> < −5
−5

5) If the sign of each term on both the sides of an inequation is changed then the inequation sign
will be reversed.
Example : −𝑥 > 5 ==> 𝑥 < −5

6) If both side of an inequation is taken reciprocal then the inequation sign will be reversed.
1 1
Example : 𝑥 > 𝑦 ==> <𝑦.
𝑥

NOTE : For an inequation the solution of the unknown variable will be expressed in the form of
Solution set or the Replacement set. And then its plotted on the number line.

PREPARED BY : A P ARUN., MSc., B.Ed., ADEEE., MDLT.,MDMT.,(NIT)

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