Representation of the Solution Set of an Inequation


Graphical representation of the solution set of an inequation:

A number line is used to represent the solution set of an inequation graphically.

First solve the linear inequation and find the solution set.

Mark it on the number line by putting a dot.

In case the solution set is infinite, then put three more dots to indicate infiniteness.


For Example: 

1. Solve the inequation 3x - 5 < 4, x ∈ N and represent the solution set graphically. 

Solution:

We have 3x - 5 < 4

⇒ 3x - 5 + 5 < 4 + 5 (Add 5 to both sides)

⇒ 3x < 9

⇒ 3x/3 < 9/3 (Divide both sides by 3)

⇒ x < 3

So, the replacement set = {1, 2, 3, 4, 5, ...}

Therefore, the solution set = {1, 2} or S = {x : x ∈ N, x < 3}

Let us mark the solution set graphically.

representation of the solution set of an inequation


Solution set is marked on the number line by dots. 



2. Solve 2x + 8 ≥ 18 


Here x ∈. W represent the inequation graphically

⇒ 2x + 8 - 8 ≥ 18 - 8 (Subtract 8 from both sides)

⇒ 2x ≥ 10

⇒ 2x/2 ≥ 10/2 (Divide both sides by 2)

⇒ x ≥ 5

Replacement set = {0, 1, 2, 3, 4, 5, 6, ...}

Therefore, solution set = {5, 6, 7, 8, 9, ...}

or, S = {x : x ∈ W, x ≥ 5}

Let us mark the solution set graphically.

inequation graphically


Solution set is marked on the number line by dots. We put three more dots indicate infiniteness of the solution set.


3. Solve -3 ≤ x ≤ 4, x ∈ I

Solution:

This contains two inequations,

-3 ≤ x and x ≤ 4

Replacement set = {..., -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ...}

Solution set for the inequation -3 ≤ x is -3, -2, -1, 0, 1, 2, ... i.e., S = {-3, -2, -1, 0, 1, 2, 3, ...} = P

And the solution set for the inequation x ≤ 4 is 4, 3, 2, 1, 0, -1, ... i.e., S = {..., -3, -2, -1, 0, 1, 2, 3, 4} = Q

Therefore, solution set of the given inequation = P ∩ Q

                          = {-3, -2, -1, 0, 1, 2, 3, 4}

or S = {x : x ∈ I, -3 ≤ x ≤ 4}

Let us represent the solution set graphically.

solution set graphically



Solution set is marked on the number line by dots.

A number line is used for representation of the solution set of an inequation.

Now, solution set S = {3, 4, 5, 6, ...} S = (x : x ∈ N, x > 3)

For Example:

4. 2x + 3 ≤ 15

⇒ 2x + 3 - 3 ≤ 15 - 3 (Subtract 3 from both sides)

⇒ 2x ≤ 12 ⇒ 2x/2 ≤ 12/2 (Divide both sides by 2)

⇒ x ≤ 6

Now, the solution set S = {1, 2, 3, 4, 5}   S' = {x : x ∈ N, x < 6}

Now, S ∩ S’ = {3, 4, 5, 6}

5. 0 < 4x - 9 ≤ 5,     x ∈ R

Solution:

Case I: 0 ≤ 4x - 9

0 + 9 ≤ 4x - 9 + 9

⇒ 9 ≤ 4x

⇒ 9/4 ≤ 4x/4

⇒ 2.25 ≤ x

⇒ 2.2 < x


Case II: 4x - 3 ≤ 9

⇒ 4x - 3 + 3 ≤ 9 + 3

⇒ 4x ≤ 12

⇒ x ≤ 3

S ∩ S' = {2.2 < x ≤ 3} x ∈ R

           = {x : x ∈ R 3 ≥ x > 2.2}

solution set of an inequation



Arrow on right shows that solution set continues.



 Inequations

What are Linear Inequality?

What are Linear Inequations?

Properties of Inequation or Inequalities

Representation of the Solution Set of an Inequation

Practice Test on Linear Inequation


 Inequations - Worksheets

Worksheet on Linear Inequations












7th Grade Math Problems

8th Grade Math Practice 

From Representation of the Solution Set of an Inequation to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.

Share this page: What’s this?

Recent Articles

  1. Formation of Greatest and Smallest Numbers | Arranging the Numbers

    May 19, 24 03:36 PM

    Formation of Greatest and Smallest Numbers
    the greatest number is formed by arranging the given digits in descending order and the smallest number by arranging them in ascending order. The position of the digit at the extreme left of a number…

    Read More

  2. Formation of Numbers with the Given Digits |Making Numbers with Digits

    May 19, 24 03:19 PM

    In formation of numbers with the given digits we may say that a number is an arranged group of digits. Numbers may be formed with or without the repetition of digits.

    Read More

  3. Arranging Numbers | Ascending Order | Descending Order |Compare Digits

    May 19, 24 02:23 PM

    Arranging Numbers
    We know, while arranging numbers from the smallest number to the largest number, then the numbers are arranged in ascending order. Vice-versa while arranging numbers from the largest number to the sma…

    Read More

  4. Comparison of Numbers | Compare Numbers Rules | Examples of Comparison

    May 19, 24 01:26 PM

    Rules for Comparison of Numbers
    Rule I: We know that a number with more digits is always greater than the number with less number of digits. Rule II: When the two numbers have the same number of digits, we start comparing the digits…

    Read More

  5. Worksheets on Comparison of Numbers | Find the Greatest Number

    May 19, 24 10:42 AM

    Comparison of Two Numbers
    In worksheets on comparison of numbers students can practice the questions for fourth grade to compare numbers. This worksheet contains questions on numbers like to find the greatest number, arranging…

    Read More